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a/_images/fe6bdb18359b5bc084d572c11aa115df8a403c44e1174e56f3e69f2934b98ec7.png b/_images/fe6bdb18359b5bc084d572c11aa115df8a403c44e1174e56f3e69f2934b98ec7.png deleted file mode 100644 index a367624a..00000000 Binary files a/_images/fe6bdb18359b5bc084d572c11aa115df8a403c44e1174e56f3e69f2934b98ec7.png and /dev/null differ diff --git a/_sources/notebooks/46_generalized_linear_models.ipynb b/_sources/notebooks/46_generalized_linear_models.ipynb index 19d05e14..52e362a8 100644 --- a/_sources/notebooks/46_generalized_linear_models.ipynb +++ b/_sources/notebooks/46_generalized_linear_models.ipynb @@ -258,7 +258,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 122, "id": "f3357c58-0d49-4019-84b7-34f16a452685", "metadata": {}, "outputs": [ @@ -292,13 +292,13 @@ "\n", "# plot the expit function, a.k.a. the logistic function\n", "xs = np.linspace(-6, 6, 500)\n", - "sns.lineplot(x=xs, y=expit(xs), ax=ax1, label=\"$\\\\text{expit}(x)$\")\n", + "sns.lineplot(x=xs, y=expit(xs), ax=ax1, label=\"$\\\\mathrm{expit}(x)$\")\n", "ax1.set_xlabel(\"$x$\")\n", "ax1.set_ylabel(\"$p$\")\n", "\n", "# plot the logit function\n", "ps = np.linspace(0, 1, 600)\n", - "sns.lineplot(x=ps, y=logit(ps), ax=ax2, label=\"$\\\\text{logit}(p)$\", color=\"C1\")\n", + "sns.lineplot(x=ps, y=logit(ps), ax=ax2, label=\"$\\\\mathrm{logit}(p)$\", color=\"C1\")\n", "ax2.set_xlabel(\"$p$\")\n", "ax2.set_ylabel(\"$x$\")\n", "\n", @@ -369,7 +369,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 123, "id": "104042bd-f21c-4e6b-8b81-bd92932ddb0c", "metadata": {}, "outputs": [ @@ -417,7 +417,7 @@ " # Plot the logistic regression model\n", " xs = np.linspace(xlims[0], xlims[1], 200)\n", " ps = expit_model(xs)\n", - " sns.lineplot(x=xs, y=ps, ax=ax, label=r\"$p(x) = \\text{expit}(\\beta_0 + \\beta_1x)$\", linewidth=2)\n", + " sns.lineplot(x=xs, y=ps, ax=ax, label=r\"$p(x) = \\mathrm{expit}(\\beta_0 + \\beta_1x)$\", linewidth=2)\n", "\n", " # Plot Bernoulli distributions at specified x positions\n", " x_positions = [2,4,5,6,8,10]\n", @@ -610,10 +610,10 @@ " Method: MLE Df Model: 1 \n", "\n", "\n", - " Date: Wed, 07 Aug 2024 Pseudo R-squ.: 0.8005 \n", + " Date: Mon, 12 Aug 2024 Pseudo R-squ.: 0.8005 \n", "\n", "\n", - " Time: 15:10:35 Log-Likelihood: -13.810 \n", + " Time: 12:44:55 Log-Likelihood: -13.810 \n", "\n", "\n", " converged: True LL-Null: -69.235 \n", @@ -641,8 +641,8 @@ "\\textbf{Dep. Variable:} & hired & \\textbf{ No. Observations: } & 100 \\\\\n", "\\textbf{Model:} & Logit & \\textbf{ Df Residuals: } & 98 \\\\\n", "\\textbf{Method:} & MLE & \\textbf{ Df Model: } & 1 \\\\\n", - "\\textbf{Date:} & Wed, 07 Aug 2024 & \\textbf{ Pseudo R-squ.: } & 0.8005 \\\\\n", - "\\textbf{Time:} & 15:10:35 & \\textbf{ Log-Likelihood: } & -13.810 \\\\\n", + "\\textbf{Date:} & Mon, 12 Aug 2024 & \\textbf{ Pseudo R-squ.: } & 0.8005 \\\\\n", + "\\textbf{Time:} & 12:44:55 & \\textbf{ Log-Likelihood: } & -13.810 \\\\\n", "\\textbf{converged:} & True & \\textbf{ LL-Null: } & -69.235 \\\\\n", "\\textbf{Covariance Type:} & nonrobust & \\textbf{ LLR p-value: } & 6.385e-26 \\\\\n", "\\bottomrule\n", @@ -669,8 +669,8 @@ "Dep. Variable: hired No. Observations: 100\n", "Model: Logit Df Residuals: 98\n", "Method: MLE Df Model: 1\n", - "Date: Wed, 07 Aug 2024 Pseudo R-squ.: 0.8005\n", - "Time: 15:10:35 Log-Likelihood: -13.810\n", + "Date: Mon, 12 Aug 2024 Pseudo R-squ.: 0.8005\n", + "Time: 12:44:55 Log-Likelihood: -13.810\n", "converged: True LL-Null: -69.235\n", "Covariance Type: nonrobust LLR p-value: 6.385e-26\n", "==============================================================================\n", @@ -784,10 +784,10 @@ " Method: MLE Df Model: 1 \n", "\n", "\n", - " Date: Wed, 07 Aug 2024 Pseudo R-squ.: 0.8005 \n", + " Date: Mon, 12 Aug 2024 Pseudo R-squ.: 0.8005 \n", "\n", "\n", - " Time: 15:10:36 Log-Likelihood: -13.810 \n", + " Time: 12:44:56 Log-Likelihood: -13.810 \n", "\n", "\n", " converged: True LL-Null: -69.235 \n", @@ -815,8 +815,8 @@ "\\textbf{Dep. Variable:} & hired & \\textbf{ No. Observations: } & 100 \\\\\n", "\\textbf{Model:} & Logit & \\textbf{ Df Residuals: } & 98 \\\\\n", "\\textbf{Method:} & MLE & \\textbf{ Df Model: } & 1 \\\\\n", - "\\textbf{Date:} & Wed, 07 Aug 2024 & \\textbf{ Pseudo R-squ.: } & 0.8005 \\\\\n", - "\\textbf{Time:} & 15:10:36 & \\textbf{ Log-Likelihood: } & -13.810 \\\\\n", + "\\textbf{Date:} & Mon, 12 Aug 2024 & \\textbf{ Pseudo R-squ.: } & 0.8005 \\\\\n", + "\\textbf{Time:} & 12:44:56 & \\textbf{ Log-Likelihood: } & -13.810 \\\\\n", "\\textbf{converged:} & True & \\textbf{ LL-Null: } & -69.235 \\\\\n", "\\textbf{Covariance Type:} & nonrobust & \\textbf{ LLR p-value: } & 6.385e-26 \\\\\n", "\\bottomrule\n", @@ -843,8 +843,8 @@ "Dep. Variable: hired No. Observations: 100\n", "Model: Logit Df Residuals: 98\n", "Method: MLE Df Model: 1\n", - "Date: Wed, 07 Aug 2024 Pseudo R-squ.: 0.8005\n", - "Time: 15:10:36 Log-Likelihood: -13.810\n", + "Date: Mon, 12 Aug 2024 Pseudo R-squ.: 0.8005\n", + "Time: 12:44:56 Log-Likelihood: -13.810\n", "converged: True LL-Null: -69.235\n", "Covariance Type: nonrobust LLR p-value: 6.385e-26\n", "==============================================================================\n", @@ -1344,10 +1344,10 @@ " Method: MLE Df Model: 1 \n", "\n", "\n", - " Date: Wed, 07 Aug 2024 Pseudo R-squ.: 0.6412 \n", + " Date: Mon, 12 Aug 2024 Pseudo R-squ.: 0.6412 \n", "\n", "\n", - " Time: 15:10:37 Log-Likelihood: -269.31 \n", + " Time: 12:44:57 Log-Likelihood: -269.31 \n", "\n", "\n", " converged: True LL-Null: -750.68 \n", @@ -1375,8 +1375,8 @@ "\\textbf{Dep. Variable:} & failures & \\textbf{ No. Observations: } & 100 \\\\\n", "\\textbf{Model:} & Poisson & \\textbf{ Df Residuals: } & 98 \\\\\n", "\\textbf{Method:} & MLE & \\textbf{ Df Model: } & 1 \\\\\n", - "\\textbf{Date:} & Wed, 07 Aug 2024 & \\textbf{ Pseudo R-squ.: } & 0.6412 \\\\\n", - "\\textbf{Time:} & 15:10:37 & \\textbf{ Log-Likelihood: } & -269.31 \\\\\n", + "\\textbf{Date:} & Mon, 12 Aug 2024 & \\textbf{ Pseudo R-squ.: } & 0.6412 \\\\\n", + "\\textbf{Time:} & 12:44:57 & \\textbf{ Log-Likelihood: } & -269.31 \\\\\n", "\\textbf{converged:} & True & \\textbf{ LL-Null: } & -750.68 \\\\\n", "\\textbf{Covariance Type:} & nonrobust & \\textbf{ LLR p-value: } & 2.271e-211 \\\\\n", "\\bottomrule\n", @@ -1399,8 +1399,8 @@ "Dep. Variable: failures No. Observations: 100\n", "Model: Poisson Df Residuals: 98\n", "Method: MLE Df Model: 1\n", - "Date: Wed, 07 Aug 2024 Pseudo R-squ.: 0.6412\n", - "Time: 15:10:37 Log-Likelihood: -269.31\n", + "Date: Mon, 12 Aug 2024 Pseudo R-squ.: 0.6412\n", + "Time: 12:44:57 Log-Likelihood: -269.31\n", "converged: True LL-Null: -750.68\n", "Covariance Type: nonrobust LLR p-value: 2.271e-211\n", "==============================================================================\n", @@ -1483,10 +1483,10 @@ " Method: MLE Df Model: 1 \n", "\n", "\n", - " Date: Wed, 07 Aug 2024 Pseudo R-squ.: 0.6412 \n", + " Date: Mon, 12 Aug 2024 Pseudo R-squ.: 0.6412 \n", "\n", "\n", - " Time: 15:10:38 Log-Likelihood: -269.31 \n", + " Time: 12:44:58 Log-Likelihood: -269.31 \n", "\n", "\n", " converged: True LL-Null: -750.68 \n", @@ -1514,8 +1514,8 @@ "\\textbf{Dep. Variable:} & failures & \\textbf{ No. Observations: } & 100 \\\\\n", "\\textbf{Model:} & Poisson & \\textbf{ Df Residuals: } & 98 \\\\\n", "\\textbf{Method:} & MLE & \\textbf{ Df Model: } & 1 \\\\\n", - "\\textbf{Date:} & Wed, 07 Aug 2024 & \\textbf{ Pseudo R-squ.: } & 0.6412 \\\\\n", - "\\textbf{Time:} & 15:10:38 & \\textbf{ Log-Likelihood: } & -269.31 \\\\\n", + "\\textbf{Date:} & Mon, 12 Aug 2024 & \\textbf{ Pseudo R-squ.: } & 0.6412 \\\\\n", + "\\textbf{Time:} & 12:44:58 & \\textbf{ Log-Likelihood: } & -269.31 \\\\\n", "\\textbf{converged:} & True & \\textbf{ LL-Null: } & -750.68 \\\\\n", "\\textbf{Covariance Type:} & nonrobust & \\textbf{ LLR p-value: } & 2.271e-211 \\\\\n", "\\bottomrule\n", @@ -1538,8 +1538,8 @@ "Dep. Variable: failures No. Observations: 100\n", "Model: Poisson Df Residuals: 98\n", "Method: MLE Df Model: 1\n", - "Date: Wed, 07 Aug 2024 Pseudo R-squ.: 0.6412\n", - "Time: 15:10:38 Log-Likelihood: -269.31\n", + "Date: Mon, 12 Aug 2024 Pseudo R-squ.: 0.6412\n", + "Time: 12:44:58 Log-Likelihood: -269.31\n", "converged: True LL-Null: -750.68\n", "Covariance Type: nonrobust LLR p-value: 2.271e-211\n", "==============================================================================\n", @@ -2894,12 +2894,99 @@ "## Exercises" ] }, + { + "cell_type": "code", + "execution_count": null, + "id": "58549438-b779-4a43-9012-ea7f5ea3afb3", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "19e1f824-f917-4e24-9f70-e1f81be2da47", + "metadata": {}, + "source": [ + "### Exercise 1: probabilities to odds and log-odds" + ] + }, + { + "cell_type": "code", + "execution_count": 111, + "id": "3cbc5fb2-e0eb-4cc1-9bd3-9188f623e835", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.4285714285714286, 98.99999999999991, 2.333333333333333)" + ] + }, + "execution_count": 111, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "0.3/(1-0.3), 0.99/(1-0.99), 0.7/(1-0.7)" + ] + }, + { + "cell_type": "code", + "execution_count": 118, + "id": "696bb24c-3bf1-4551-83da-3df058f3b959", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(-0.8472978603872036, 4.595119850134589, 0.8472978603872034)" + ] + }, + "execution_count": 118, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "logit(0.3), logit(0.99), logit(0.7)" + ] + }, + { + "cell_type": "markdown", + "id": "178717ef-5d7e-4afc-ab5a-25a306cad5a5", + "metadata": {}, + "source": [ + "### Exercise 2: log-odds to probabilities" + ] + }, + { + "cell_type": "code", + "execution_count": 119, + "id": "94267802-427f-4791-bb82-1e42a274e566", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.2689414213699951, 0.7310585786300049, 0.8807970779778823)" + ] + }, + "execution_count": 119, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expit(-1), expit(1), expit(2)" + ] + }, { "cell_type": "markdown", "id": "fb23931d-ab9b-4e57-9876-0ca3c17b8e48", "metadata": {}, "source": [ - "### Exercise 1: students pass or fail" + "### Exercise 3: students pass or fail" ] }, { @@ -3038,7 +3125,7 @@ "id": "d8eebdfa-2b50-403c-96c4-60840e8ea47e", "metadata": {}, "source": [ - "### Exercise 2: titanic survival data\n", + "### Exercise 4: titanic survival data\n", "\n", "Fit a logistic regression model that calculates the probability of survival for people who were on the Titanic,\n", "based on the data in `datasets/exercises/titanic.csv`. Use the variables `age`, `sex`, and `pclass` as predictors.\n", @@ -3137,7 +3224,7 @@ "id": "8e84a8f5-8616-4bc7-a3aa-dcbab67eef1e", "metadata": {}, "source": [ - "### Exercise 3: asthma attacks\n", + "### Exercise 5: asthma attacks\n", "\n", "Fit a Poisson regression model to the `../datasets/exercises/asthma.csv` dataset.\n", "\n", @@ -3336,7 +3423,7 @@ "id": "f83eb7a2-20af-4da8-af87-a4b8e956ba97", "metadata": {}, "source": [ - "### Exercise 4: student admissions dataset\n", + "### Exercise 6: student admissions dataset\n", "\n", "The dataset `datasets/exercises/binary.csv` contains information\n", "about the acceptance decision for 400 students to a prestigious school.\n", @@ -3498,7 +3585,7 @@ "id": "a876994d-fea4-48bd-8964-d1f81fd299aa", "metadata": {}, "source": [ - "### Exercise 5: ship accidents\n", + "### Exercise 7: ship accidents\n", "\n", "https://rdrr.io/cran/AER/man/ShipAccidents.html\n", "\n", @@ -3572,40 +3659,40 @@ " \n", " \n", " \n", - " 29\n", - " 0\n", - " 52\n", - " 44\n", + " 128\n", + " 1\n", + " 50\n", " 49\n", + " 56\n", " 0\n", - " 0\n", + " 56\n", " \n", " \n", - " 64\n", + " 41\n", " 0\n", - " 50\n", - " 42\n", - " 50\n", + " 55\n", + " 59\n", + " 62\n", " 0\n", " 0\n", " \n", " \n", - " 72\n", - " 0\n", - " 73\n", + " 182\n", + " 1\n", + " 52\n", " 67\n", - " 71\n", + " 57\n", " 1\n", - " 0\n", + " 57\n", " \n", " \n", - " 143\n", + " 103\n", " 1\n", - " 47\n", - " 57\n", - " 48\n", + " 63\n", + " 52\n", + " 54\n", " 0\n", - " 48\n", + " 54\n", " \n", " \n", "\n", @@ -3613,10 +3700,10 @@ ], "text/plain": [ " female read write math hon femalexmath\n", - "29 0 52 44 49 0 0\n", - "64 0 50 42 50 0 0\n", - "72 0 73 67 71 1 0\n", - "143 1 47 57 48 0 48" + "128 1 50 49 56 0 56\n", + "41 0 55 59 62 0 0\n", + "182 1 52 67 57 1 57\n", + "103 1 63 52 54 0 54" ] }, "execution_count": 82, @@ -4046,7 +4133,7 @@ "So the model equation is \n", "\n", "$$\n", - " \\log(p/(1-p)) = \\text{logit}(p) = -9.793942 + .1563404 \\cdot \\tt{math}\n", + " \\log(p/(1-p)) = \\texttt{logit}(p) = -9.793942 + .1563404 \\cdot \\texttt{math}\n", "$$" ] }, @@ -4234,127 +4321,41 @@ "metadata": {}, "outputs": [ { - "data": { - "text/html": [ - "
\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
idgenderethnicschoolmathprlangprmathncelangncebilingdaysabs
01001MHispanicAlpha633656.98883142.45085924
11002MHispanicAlpha274437.09415846.82058724
21003FHispanicAlpha203832.27545543.56657422
31004FHispanicAlpha163829.05671743.56657423
41005FHispanicAlpha2146.74804827.24847433
\n", - "
" - ], - "text/plain": [ - " id gender ethnic school mathpr langpr mathnce langnce biling \\\n", - "0 1001 M Hispanic Alpha 63 36 56.988831 42.450859 2 \n", - "1 1002 M Hispanic Alpha 27 44 37.094158 46.820587 2 \n", - "2 1003 F Hispanic Alpha 20 38 32.275455 43.566574 2 \n", - "3 1004 F Hispanic Alpha 16 38 29.056717 43.566574 2 \n", - "4 1005 F Hispanic Alpha 2 14 6.748048 27.248474 3 \n", - "\n", - " daysabs \n", - "0 4 \n", - "1 4 \n", - "2 2 \n", - "3 3 \n", - "4 3 " - ] - }, - "execution_count": 102, - "metadata": {}, - "output_type": "execute_result" + "ename": "URLError", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mgaierror\u001b[0m Traceback (most recent call last)", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:1346\u001b[0m, in \u001b[0;36mAbstractHTTPHandler.do_open\u001b[0;34m(self, http_class, req, **http_conn_args)\u001b[0m\n\u001b[1;32m 1345\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m-> 1346\u001b[0m \u001b[43mh\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrequest\u001b[49m\u001b[43m(\u001b[49m\u001b[43mreq\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_method\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mreq\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mselector\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mreq\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdata\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mheaders\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 1347\u001b[0m \u001b[43m \u001b[49m\u001b[43mencode_chunked\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mreq\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mhas_header\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mTransfer-encoding\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 1348\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mOSError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m err: \u001b[38;5;66;03m# timeout error\u001b[39;00m\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:1253\u001b[0m, in \u001b[0;36mHTTPConnection.request\u001b[0;34m(self, method, url, body, headers, encode_chunked)\u001b[0m\n\u001b[1;32m 1252\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"Send a complete request to the server.\"\"\"\u001b[39;00m\n\u001b[0;32m-> 1253\u001b[0m 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\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mendheaders\u001b[49m\u001b[43m(\u001b[49m\u001b[43mbody\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mencode_chunked\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mencode_chunked\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:1248\u001b[0m, in \u001b[0;36mHTTPConnection.endheaders\u001b[0;34m(self, message_body, encode_chunked)\u001b[0m\n\u001b[1;32m 1247\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m CannotSendHeader()\n\u001b[0;32m-> 1248\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_send_output\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmessage_body\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mencode_chunked\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mencode_chunked\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:1008\u001b[0m, in \u001b[0;36mHTTPConnection._send_output\u001b[0;34m(self, message_body, encode_chunked)\u001b[0m\n\u001b[1;32m 1007\u001b[0m \u001b[38;5;28;01mdel\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_buffer[:]\n\u001b[0;32m-> 1008\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msend\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmsg\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 1010\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m message_body \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 1011\u001b[0m \n\u001b[1;32m 1012\u001b[0m \u001b[38;5;66;03m# create a consistent interface to message_body\u001b[39;00m\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:948\u001b[0m, in \u001b[0;36mHTTPConnection.send\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m 947\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mauto_open:\n\u001b[0;32m--> 948\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mconnect\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 949\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:1415\u001b[0m, in \u001b[0;36mHTTPSConnection.connect\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 1413\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mConnect to a host on a given (SSL) port.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m-> 1415\u001b[0m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mconnect\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 1417\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_tunnel_host:\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:919\u001b[0m, in \u001b[0;36mHTTPConnection.connect\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 918\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"Connect to the host and port specified in __init__.\"\"\"\u001b[39;00m\n\u001b[0;32m--> 919\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39msock \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_create_connection\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 920\u001b[0m \u001b[43m \u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mhost\u001b[49m\u001b[43m,\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mport\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m 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\u001b[49m\u001b[43mport\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mSOCK_STREAM\u001b[49m\u001b[43m)\u001b[49m:\n\u001b[1;32m 823\u001b[0m af, socktype, proto, canonname, sa \u001b[38;5;241m=\u001b[39m res\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/socket.py:953\u001b[0m, in \u001b[0;36mgetaddrinfo\u001b[0;34m(host, port, family, type, proto, flags)\u001b[0m\n\u001b[1;32m 952\u001b[0m addrlist \u001b[38;5;241m=\u001b[39m []\n\u001b[0;32m--> 953\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m res \u001b[38;5;129;01min\u001b[39;00m \u001b[43m_socket\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgetaddrinfo\u001b[49m\u001b[43m(\u001b[49m\u001b[43mhost\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mport\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfamily\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mtype\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mproto\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mflags\u001b[49m\u001b[43m)\u001b[49m:\n\u001b[1;32m 954\u001b[0m af, socktype, proto, canonname, sa \u001b[38;5;241m=\u001b[39m res\n", + "\u001b[0;31mgaierror\u001b[0m: [Errno 8] nodename nor servname provided, or not known", + "\nDuring handling of the above exception, another exception occurred:\n", + "\u001b[0;31mURLError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[102], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m lahigh_raw \u001b[38;5;241m=\u001b[39m \u001b[43mpd\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mread_stata\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mhttps://stats.idre.ucla.edu/stat/stata/notes/lahigh.dta\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m 2\u001b[0m lahigh \u001b[38;5;241m=\u001b[39m lahigh_raw\u001b[38;5;241m.\u001b[39mconvert_dtypes()\n\u001b[1;32m 4\u001b[0m lahigh[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mgender\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m lahigh[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mgender\u001b[39m\u001b[38;5;124m\"\u001b[39m]\u001b[38;5;241m.\u001b[39mastype(\u001b[38;5;28mobject\u001b[39m)\u001b[38;5;241m.\u001b[39mreplace({\u001b[38;5;241m1\u001b[39m:\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mF\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;241m2\u001b[39m:\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mM\u001b[39m\u001b[38;5;124m\"\u001b[39m})\n", + "File \u001b[0;32m~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/stata.py:2109\u001b[0m, in \u001b[0;36mread_stata\u001b[0;34m(filepath_or_buffer, convert_dates, convert_categoricals, index_col, convert_missing, preserve_dtypes, columns, order_categoricals, chunksize, iterator, compression, storage_options)\u001b[0m\n\u001b[1;32m 2106\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m reader\n\u001b[1;32m 2108\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m reader:\n\u001b[0;32m-> 2109\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mreader\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mread\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/stata.py:1683\u001b[0m, in \u001b[0;36mStataReader.read\u001b[0;34m(self, nrows, convert_dates, convert_categoricals, index_col, convert_missing, preserve_dtypes, columns, order_categoricals)\u001b[0m\n\u001b[1;32m 1671\u001b[0m \u001b[38;5;129m@Appender\u001b[39m(_read_method_doc)\n\u001b[1;32m 1672\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mread\u001b[39m(\n\u001b[1;32m 1673\u001b[0m \u001b[38;5;28mself\u001b[39m,\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 1681\u001b[0m order_categoricals: \u001b[38;5;28mbool\u001b[39m \u001b[38;5;241m|\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m,\n\u001b[1;32m 1682\u001b[0m ) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m DataFrame:\n\u001b[0;32m-> 1683\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_ensure_open\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 1685\u001b[0m \u001b[38;5;66;03m# Handle options\u001b[39;00m\n\u001b[1;32m 1686\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m convert_dates \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n", + "File \u001b[0;32m~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/stata.py:1175\u001b[0m, in \u001b[0;36mStataReader._ensure_open\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 1171\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 1172\u001b[0m \u001b[38;5;124;03mEnsure the file has been opened and its header data read.\u001b[39;00m\n\u001b[1;32m 1173\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 1174\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mhasattr\u001b[39m(\u001b[38;5;28mself\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m_path_or_buf\u001b[39m\u001b[38;5;124m\"\u001b[39m):\n\u001b[0;32m-> 1175\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_open_file\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/stata.py:1188\u001b[0m, in \u001b[0;36mStataReader._open_file\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 1181\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_entered:\n\u001b[1;32m 1182\u001b[0m warnings\u001b[38;5;241m.\u001b[39mwarn(\n\u001b[1;32m 1183\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mStataReader is being used without using a context manager. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 1184\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mUsing StataReader as a context manager is the only supported method.\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m 1185\u001b[0m \u001b[38;5;167;01mResourceWarning\u001b[39;00m,\n\u001b[1;32m 1186\u001b[0m stacklevel\u001b[38;5;241m=\u001b[39mfind_stack_level(),\n\u001b[1;32m 1187\u001b[0m )\n\u001b[0;32m-> 1188\u001b[0m handles \u001b[38;5;241m=\u001b[39m \u001b[43mget_handle\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 1189\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_original_path_or_buf\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 1190\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mrb\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m 1191\u001b[0m \u001b[43m \u001b[49m\u001b[43mstorage_options\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_storage_options\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 1192\u001b[0m \u001b[43m \u001b[49m\u001b[43mis_text\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mFalse\u001b[39;49;00m\u001b[43m,\u001b[49m\n\u001b[1;32m 1193\u001b[0m \u001b[43m \u001b[49m\u001b[43mcompression\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_compression\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 1194\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 1195\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mhasattr\u001b[39m(handles\u001b[38;5;241m.\u001b[39mhandle, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mseekable\u001b[39m\u001b[38;5;124m\"\u001b[39m) \u001b[38;5;129;01mand\u001b[39;00m handles\u001b[38;5;241m.\u001b[39mhandle\u001b[38;5;241m.\u001b[39mseekable():\n\u001b[1;32m 1196\u001b[0m \u001b[38;5;66;03m# If the handle is directly seekable, use it without an extra copy.\u001b[39;00m\n\u001b[1;32m 1197\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_path_or_buf \u001b[38;5;241m=\u001b[39m handles\u001b[38;5;241m.\u001b[39mhandle\n", + "File \u001b[0;32m~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/common.py:728\u001b[0m, in \u001b[0;36mget_handle\u001b[0;34m(path_or_buf, mode, encoding, compression, memory_map, is_text, errors, storage_options)\u001b[0m\n\u001b[1;32m 725\u001b[0m codecs\u001b[38;5;241m.\u001b[39mlookup_error(errors)\n\u001b[1;32m 727\u001b[0m \u001b[38;5;66;03m# open URLs\u001b[39;00m\n\u001b[0;32m--> 728\u001b[0m ioargs \u001b[38;5;241m=\u001b[39m \u001b[43m_get_filepath_or_buffer\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 729\u001b[0m \u001b[43m \u001b[49m\u001b[43mpath_or_buf\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 730\u001b[0m \u001b[43m \u001b[49m\u001b[43mencoding\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mencoding\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 731\u001b[0m \u001b[43m \u001b[49m\u001b[43mcompression\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcompression\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 732\u001b[0m \u001b[43m \u001b[49m\u001b[43mmode\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mmode\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 733\u001b[0m \u001b[43m \u001b[49m\u001b[43mstorage_options\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mstorage_options\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 734\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 736\u001b[0m handle \u001b[38;5;241m=\u001b[39m ioargs\u001b[38;5;241m.\u001b[39mfilepath_or_buffer\n\u001b[1;32m 737\u001b[0m handles: \u001b[38;5;28mlist\u001b[39m[BaseBuffer]\n", + "File \u001b[0;32m~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/common.py:384\u001b[0m, in \u001b[0;36m_get_filepath_or_buffer\u001b[0;34m(filepath_or_buffer, encoding, compression, mode, storage_options)\u001b[0m\n\u001b[1;32m 382\u001b[0m \u001b[38;5;66;03m# assuming storage_options is to be interpreted as headers\u001b[39;00m\n\u001b[1;32m 383\u001b[0m req_info \u001b[38;5;241m=\u001b[39m urllib\u001b[38;5;241m.\u001b[39mrequest\u001b[38;5;241m.\u001b[39mRequest(filepath_or_buffer, headers\u001b[38;5;241m=\u001b[39mstorage_options)\n\u001b[0;32m--> 384\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[43murlopen\u001b[49m\u001b[43m(\u001b[49m\u001b[43mreq_info\u001b[49m\u001b[43m)\u001b[49m \u001b[38;5;28;01mas\u001b[39;00m req:\n\u001b[1;32m 385\u001b[0m content_encoding \u001b[38;5;241m=\u001b[39m req\u001b[38;5;241m.\u001b[39mheaders\u001b[38;5;241m.\u001b[39mget(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mContent-Encoding\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m)\n\u001b[1;32m 386\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m content_encoding \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mgzip\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[1;32m 387\u001b[0m \u001b[38;5;66;03m# Override compression based on Content-Encoding header\u001b[39;00m\n", + "File \u001b[0;32m~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/common.py:289\u001b[0m, in \u001b[0;36murlopen\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 283\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 284\u001b[0m \u001b[38;5;124;03mLazy-import wrapper for stdlib urlopen, as that imports a big chunk of\u001b[39;00m\n\u001b[1;32m 285\u001b[0m \u001b[38;5;124;03mthe stdlib.\u001b[39;00m\n\u001b[1;32m 286\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 287\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01murllib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mrequest\u001b[39;00m\n\u001b[0;32m--> 289\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43murllib\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrequest\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43murlopen\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:214\u001b[0m, in \u001b[0;36murlopen\u001b[0;34m(url, data, timeout, cafile, capath, cadefault, context)\u001b[0m\n\u001b[1;32m 212\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 213\u001b[0m opener \u001b[38;5;241m=\u001b[39m _opener\n\u001b[0;32m--> 214\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mopener\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mopen\u001b[49m\u001b[43m(\u001b[49m\u001b[43murl\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtimeout\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:517\u001b[0m, in \u001b[0;36mOpenerDirector.open\u001b[0;34m(self, fullurl, data, timeout)\u001b[0m\n\u001b[1;32m 514\u001b[0m req \u001b[38;5;241m=\u001b[39m meth(req)\n\u001b[1;32m 516\u001b[0m sys\u001b[38;5;241m.\u001b[39maudit(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124murllib.Request\u001b[39m\u001b[38;5;124m'\u001b[39m, req\u001b[38;5;241m.\u001b[39mfull_url, req\u001b[38;5;241m.\u001b[39mdata, req\u001b[38;5;241m.\u001b[39mheaders, req\u001b[38;5;241m.\u001b[39mget_method())\n\u001b[0;32m--> 517\u001b[0m response \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_open\u001b[49m\u001b[43m(\u001b[49m\u001b[43mreq\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdata\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 519\u001b[0m \u001b[38;5;66;03m# post-process response\u001b[39;00m\n\u001b[1;32m 520\u001b[0m meth_name \u001b[38;5;241m=\u001b[39m protocol\u001b[38;5;241m+\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m_response\u001b[39m\u001b[38;5;124m\"\u001b[39m\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:534\u001b[0m, in \u001b[0;36mOpenerDirector._open\u001b[0;34m(self, req, data)\u001b[0m\n\u001b[1;32m 531\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m result\n\u001b[1;32m 533\u001b[0m protocol \u001b[38;5;241m=\u001b[39m req\u001b[38;5;241m.\u001b[39mtype\n\u001b[0;32m--> 534\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_call_chain\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mhandle_open\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprotocol\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprotocol\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m+\u001b[39;49m\n\u001b[1;32m 535\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m_open\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mreq\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 536\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m result:\n\u001b[1;32m 537\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m result\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:494\u001b[0m, in \u001b[0;36mOpenerDirector._call_chain\u001b[0;34m(self, chain, kind, meth_name, *args)\u001b[0m\n\u001b[1;32m 492\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m handler \u001b[38;5;129;01min\u001b[39;00m handlers:\n\u001b[1;32m 493\u001b[0m func \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(handler, meth_name)\n\u001b[0;32m--> 494\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 495\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m result \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 496\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m result\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:1389\u001b[0m, in \u001b[0;36mHTTPSHandler.https_open\u001b[0;34m(self, req)\u001b[0m\n\u001b[1;32m 1388\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mhttps_open\u001b[39m(\u001b[38;5;28mself\u001b[39m, req):\n\u001b[0;32m-> 1389\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdo_open\u001b[49m\u001b[43m(\u001b[49m\u001b[43mhttp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mclient\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mHTTPSConnection\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mreq\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 1390\u001b[0m \u001b[43m \u001b[49m\u001b[43mcontext\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_context\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcheck_hostname\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_check_hostname\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:1349\u001b[0m, in \u001b[0;36mAbstractHTTPHandler.do_open\u001b[0;34m(self, http_class, req, **http_conn_args)\u001b[0m\n\u001b[1;32m 1346\u001b[0m h\u001b[38;5;241m.\u001b[39mrequest(req\u001b[38;5;241m.\u001b[39mget_method(), req\u001b[38;5;241m.\u001b[39mselector, req\u001b[38;5;241m.\u001b[39mdata, headers,\n\u001b[1;32m 1347\u001b[0m encode_chunked\u001b[38;5;241m=\u001b[39mreq\u001b[38;5;241m.\u001b[39mhas_header(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mTransfer-encoding\u001b[39m\u001b[38;5;124m'\u001b[39m))\n\u001b[1;32m 1348\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mOSError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m err: \u001b[38;5;66;03m# timeout error\u001b[39;00m\n\u001b[0;32m-> 1349\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m URLError(err)\n\u001b[1;32m 1350\u001b[0m r \u001b[38;5;241m=\u001b[39m h\u001b[38;5;241m.\u001b[39mgetresponse()\n\u001b[1;32m 1351\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m:\n", + "\u001b[0;31mURLError\u001b[0m: " + ] } ], "source": [ @@ -4376,34 +4377,10 @@ }, { "cell_type": "code", - "execution_count": 103, + "execution_count": null, "id": "1cfa5b56-a7cd-4d34-bdbd-8933397854ad", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Optimization terminated successfully.\n", - " Current function value: 4.898642\n", - " Iterations 5\n" - ] - }, - { - "data": { - "text/plain": [ - "Intercept 2.687666\n", - "C(gender)[T.M] -0.400921\n", - "mathnce -0.003523\n", - "langnce -0.012152\n", - "dtype: float64" - ] - }, - "execution_count": 103, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "formula = \"daysabs ~ 1 + mathnce + langnce + C(gender)\"\n", "prlahigh = smf.poisson(formula, data=lahigh).fit()\n", @@ -4412,24 +4389,10 @@ }, { "cell_type": "code", - "execution_count": 104, + "execution_count": null, "id": "7973597c-b205-475b-81cc-7fb25978a51f", "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "C(gender)[T.M] 0.669703\n", - "mathnce 0.996483\n", - "langnce 0.987921\n", - "dtype: float64" - ] - }, - "execution_count": 104, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "# IRR\n", "np.exp(prlahigh.params[1:])" @@ -4437,23 +4400,10 @@ }, { "cell_type": "code", - "execution_count": 105, + "execution_count": null, "id": "4e2a7e9d-2a83-4e06-ad2f-2a44bba73b1d", "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0 0.609079\n", - "1 0.736361\n", - "Name: C(gender)[T.M], dtype: float64" - ] - }, - "execution_count": 105, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "# CI for IRR F \n", "np.exp(prlahigh.conf_int().loc[\"C(gender)[T.M]\"])" @@ -4461,7 +4411,7 @@ }, { "cell_type": "code", - "execution_count": 106, + "execution_count": null, "id": "5ec05dc5-c4a8-410f-a48c-022c8a026ee5", "metadata": {}, "outputs": [], @@ -4482,7 +4432,7 @@ }, { "cell_type": "code", - "execution_count": 107, + "execution_count": null, "id": "67d0a936-e139-4e0d-aad3-fae2dc7b985d", "metadata": {}, "outputs": [], @@ -4503,34 +4453,10 @@ }, { "cell_type": "code", - "execution_count": 108, + "execution_count": null, "id": "8d620ae9-514d-4e46-91cc-a3e451950273", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Optimization terminated successfully.\n", - " Current function value: 4.898642\n", - " Iterations 5\n" - ] - }, - { - "data": { - "text/plain": [ - "Intercept 2.286745\n", - "C(gender, Treatment(1))[T.F] 0.400921\n", - "mathnce -0.003523\n", - "langnce -0.012152\n", - "dtype: float64" - ] - }, - "execution_count": 108, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "# Code to get exactly the same numbers as in\n", "# https://stats.oarc.ucla.edu/stata/output/poisson-regression/ \n", diff --git a/_sources/notebooks/50_extra_bayesian_stuff.ipynb b/_sources/notebooks/50_extra_bayesian_stuff.ipynb new file mode 100644 index 00000000..f43f92c9 --- /dev/null +++ b/_sources/notebooks/50_extra_bayesian_stuff.ipynb @@ -0,0 +1,247 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "95a6eda2-a640-4817-9eaf-88bad67ca3d9", + "metadata": {}, + "source": [ + "# Chapter 5: Extra code, drafts, and cut material" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b818a09a-90ac-408e-b39c-f30dd038c6fc", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "1ad57ed2-8583-4d1f-a16c-ddd481ee3e5f", + "metadata": {}, + "source": [ + "## Bayesian p-value" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "48fc8af8-bfee-4239-8ae7-8419c072ed21", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [beta0, beta1, sigma]\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
\n", + " \n", + " 100.00% [12000/12000 00:06<00:00 Sampling 4 chains, 0 divergences]\n", + "
\n", + " " + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 17 seconds.\n" + ] + } + ], + "source": [ + "import pymc as pm\n", + "import numpy as np\n", + "import arviz as az\n", + "\n", + "# Simulated data\n", + "np.random.seed(42)\n", + "x = np.random.normal(0, 1, 100)\n", + "y = 3 + 2 * x + np.random.normal(0, 1, 100)\n", + "\n", + "# Bayesian Linear Regression Model\n", + "with pm.Model() as model:\n", + " # Priors\n", + " beta0 = pm.Normal(\"beta0\", mu=0, sigma=10)\n", + " beta1 = pm.Normal(\"beta1\", mu=0, sigma=10)\n", + " sigma = pm.HalfNormal(\"sigma\", sigma=1)\n", + " \n", + " # Likelihood\n", + " mu = beta0 + beta1 * x\n", + " y_obs = pm.Normal(\"y_obs\", mu=mu, sigma=sigma, observed=y)\n", + " \n", + " # Sampling\n", + " trace = pm.sample(2000, return_inferencedata=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "623fce90-4525-40df-b2ff-498d801a2a3b", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [y_obs]\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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\n", + " " + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Posterior Predictive Check\n", + "# with model:\n", + "# ppc = pm.sample_posterior_predictive(trace) \n", + "# Posterior Predictive Check\n", + "ppc = pm.sample_posterior_predictive(trace, model=model)\n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "b526666e-ace3-4b0c-af87-bd0fbcb95aad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bayesian p-value: 0.4925\n" + ] + } + ], + "source": [ + "# Extract the posterior predictive samples for 'y_obs'\n", + "y_rep = ppc.posterior_predictive[\"y_obs\"].values\n", + "\n", + "# Calculate Bayesian p-value for the slope\n", + "test_stat_observed = np.mean(y) # Example test statistic\n", + "test_stat_rep = np.mean(y_rep, axis=1)\n", + "bayesian_p_value = np.mean(test_stat_rep >= test_stat_observed)\n", + "print(\"Bayesian p-value:\", bayesian_p_value)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d446b936-8610-4914-975e-ada7d078db7e", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/notebooks/51_intro_to_Bayesian_stats.ipynb b/_sources/notebooks/51_intro_to_Bayesian_stats.ipynb new file mode 100644 index 00000000..9a2216f5 --- /dev/null +++ b/_sources/notebooks/51_intro_to_Bayesian_stats.ipynb @@ -0,0 +1,531 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c53eb8f5-80a7-4330-9f13-63220177fcc0", + "metadata": { + "tags": [] + }, + "source": [ + "# Section 5.1 — Introduction to Bayesian statistics\n", + "\n", + "This notebook contains the code examples from [Section 5.1 Introduction to Bayesian statistics]() from the **No Bullshit Guide to Statistics**." + ] + }, + { + "cell_type": "markdown", + "id": "a2d8dda2-58a9-424e-9fb3-32ad6e8777d8", + "metadata": { + "tags": [] + }, + "source": [ + "#### Notebook setup" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "aea0223e-aee9-4875-a714-897b6646baaa", + "metadata": {}, + "outputs": [], + "source": [ + "# load Python modules\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "efd86c5a-c9d2-4eab-b67d-a65e39b23ef2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Figures setup\n", + "plt.clf() # needed otherwise `sns.set_theme` doesn\"t work\n", + "from plot_helpers import RCPARAMS\n", + "RCPARAMS.update({\"figure.figsize\": (5, 3)}) # good for screen\n", + "# RCPARAMS.update({\"figure.figsize\": (5, 1.6)}) # good for print\n", + "sns.set_theme(\n", + " context=\"paper\",\n", + " style=\"whitegrid\",\n", + " palette=\"colorblind\",\n", + " rc=RCPARAMS,\n", + ")\n", + "\n", + "# High-resolution please\n", + "%config InlineBackend.figure_format = \"retina\"\n", + "\n", + "# Where to store figures\n", + "DESTDIR = \"figures/bayesian/intro\"" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "df811a10-417d-4389-8bff-30e59b5f6aef", + "metadata": {}, + "outputs": [], + "source": [ + "# set random seed for repeatability\n", + "np.random.seed(42)\n", + "#######################################################" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "6b7ea783-c07c-4135-a358-29af4b4cdef9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 338, + "width": 428 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# via https://nbviewer.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers\n", + "# /blob/master/Chapter1_Introduction/Ch1_Introduction_PyMC3.ipynb\n", + "from scipy.stats import beta\n", + "from scipy.stats import bernoulli\n", + "\n", + "n_trials = [0, 1, 2, 3, 4, 5, 8, 15, 50, 500]\n", + "data = bernoulli.rvs(0.5, size=n_trials[-1])\n", + "x = np.linspace(0, 1, 100)\n", + "\n", + "# For the already prepared, I'm using Binomial's conj. prior.\n", + "for k, N in enumerate(n_trials):\n", + " sx = plt.subplot(len(n_trials)//2, 2, k+1)\n", + " plt.xlabel(\"$p$, probability of heads\") \\\n", + " if k in [0, len(n_trials)-1] else None\n", + " plt.setp(sx.get_yticklabels(), visible=False)\n", + " heads = data[:N].sum()\n", + " y = beta.pdf(x, 1 + heads, 1 + N - heads)\n", + " plt.plot(x, y, label=\"observe %d tosses,\\n %d heads\" % (N, heads))\n", + " plt.fill_between(x, 0, y, color=\"#348ABD\", alpha=0.4)\n", + " plt.vlines(0.5, 0, 4, color=\"k\", linestyles=\"--\", lw=1)\n", + "\n", + " leg = plt.legend()\n", + " leg.get_frame().set_alpha(0.4)\n", + " plt.autoscale(tight=True)\n", + "\n", + "\n", + "plt.suptitle(\"Bayesian updating of posterior probabilities\",\n", + " y=1.02,\n", + " fontsize=14);" + ] + }, + { + "cell_type": "markdown", + "id": "711d2840-3c20-45a0-b3c6-330612efdcc4", + "metadata": {}, + "source": [ + "## Example 1: estimating the probability of a biased coin" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2790bdf7-ab66-462f-89f7-f9b43e95240d", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fb69d135-09ac-4c4a-91a2-f3c59e53e2d2", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "23543fca-71ed-418e-af17-62d0d92c68e4", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.special import binom, betaln\n", + "\n", + "def beta_binom(prior, y):\n", + " \"\"\"\n", + " Compute the marginal-log-likelihood for a beta-binomial model,\n", + " analytically.\n", + "\n", + " prior : tuple\n", + " tuple of alpha and beta parameter for the prior (beta distribution)\n", + " y : array\n", + " array with \"1\" and \"0\" corresponding to the success and fails respectively\n", + " \"\"\"\n", + " α, β = prior\n", + " success = np.sum(y)\n", + " trials = len(y)\n", + " return np.log(binom(trials, success)) + betaln(α + success, β+trials-success) - betaln(α, β)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "2681f3f4-2057-441d-84f1-47bc83569253", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import stats\n", + "\n", + "\n", + "def beta_binom_harmonic(prior, y, s=10000):\n", + " \"\"\"\n", + " Compute the marginal-log-likelihood for a beta-binomial model,\n", + " using the harmonic mean estimator.\n", + "\n", + " prior : tuple\n", + " tuple of alpha and beta parameter for the prior (beta distribution)\n", + " y : array\n", + " array with \"1\" and \"0\" corresponding to the success and fails respectively\n", + " s : int\n", + " number of samples from the posterior\n", + " \"\"\"\n", + " α, β = prior\n", + " success = np.sum(y)\n", + " trials = len(y)\n", + " posterior_samples = stats.beta(α + success, β+trials-success).rvs(s)\n", + " log_likelihood = stats.binom.logpmf(success, trials, posterior_samples)\n", + " return 1/np.mean(1/log_likelihood)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "34d28c13-469e-4f40-8567-687a2ec3ba33", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 274, + "width": 391 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "data = [np.repeat([1, 0], rep)\n", + " for rep in ((1, 0), (1, 1), (5, 5), (100, 100))]\n", + "priors = ((1, 1), (100, 100), (1, 2), (1, 200))\n", + "\n", + "x_names = [repr((sum(x), len(x)-sum(x))) for x in data]\n", + "y_names = [\"Beta\" + repr(x) for x in priors]\n", + "\n", + "fig, ax = plt.subplots()\n", + "error_matrix = np.zeros((len(priors), len(data)))\n", + "for i, prior in enumerate(priors):\n", + " for j, y in enumerate(data):\n", + " error_matrix[i, j] = 100 * \\\n", + " (1 - (beta_binom_harmonic(prior, y) / beta_binom(prior, y)))\n", + "im = ax.imshow(error_matrix, cmap='viridis')\n", + "ax.set_xticks(np.arange(len(x_names)))\n", + "ax.set_yticks(np.arange(len(y_names)))\n", + "ax.set_xticklabels(x_names)\n", + "ax.set_yticklabels(y_names)\n", + "fig.colorbar(im)\n", + "# plt.savefig(\"img/chp11/harmonic_mean_heatmap.png\")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "b5db0294-3643-4621-840d-b7ff4c9f4708", + "metadata": {}, + "outputs": [], + "source": [ + "def normal_harmonic(sd_0, sd_1, y, s=10000):\n", + " post_tau = 1/sd_0**2 + 1/sd_1**2\n", + " posterior_samples = stats.norm(loc=(y/sd_1**2)/post_tau, scale=(1/post_tau)**0.5).rvs((s, len(x)))\n", + " log_likelihood = stats.norm.logpdf(loc=x, scale=sd_1, x=posterior_samples).sum(1)\n", + " return 1/np.mean(1/log_likelihood)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "e4c076a2-8635-4c22-bbb1-26b1fc4587e7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-1.2655121234846454" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "σ_0 = 1\n", + "σ_1 = 1\n", + "y = np.array([0])\n", + "stats.norm.logpdf(loc=0, scale=(σ_0**2+σ_1**2)**0.5, x=y).sum()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "f8b33f54-4cd5-4c2b-ac4d-f09a5beaa3f0", + "metadata": {}, + "outputs": [], + "source": [ + "def posterior_ml_ic_normal(σ_0=1, σ_1=1, y=[1]):\n", + " n = len(y)\n", + " var_μ = 1/((1/σ_0**2) + (n/σ_1**2))\n", + " μ = var_μ * np.sum(y)/σ_1**2\n", + " σ_μ = var_μ**0.5\n", + "\n", + " posterior = stats.norm(loc=μ, scale=σ_μ)\n", + " samples = posterior.rvs(size=(2, 1000))\n", + " log_likelihood = stats.norm(loc=samples[:, :, None], scale=σ_1).logpdf(y)\n", + " idata = az.from_dict(log_likelihood={'o': log_likelihood})\n", + "\n", + " log_ml = stats.norm.logpdf(loc=0, scale=(σ_0**2+σ_1**2)**0.5, x=y).sum()\n", + " \n", + " x = np.linspace(-5, 6, 300)\n", + " density = posterior.pdf(x)\n", + " \n", + " return μ, σ_μ, x, density, log_ml, az.waic(idata).elpd_waic, az.loo(idata, reff=1).elpd_loo" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6b1323f6-af88-4dfb-a5c1-537929e87ffb", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "2dc63628-2535-41c6-a24f-49d11c2c7329", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 0, 'μ')" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 611, + "width": 1011 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "import arviz as az\n", + "\n", + "y = np.array([ 0.65225338, -0.06122589, 0.27745188, 1.38026371, -0.72751008,\n", + " -1.10323829, 2.07122286, -0.52652711, 0.51528113, 0.71297661])\n", + "\n", + "_, ax = plt.subplots(3, figsize=(10, 6), sharex=True, sharey=True,\n", + " constrained_layout=True)\n", + "\n", + "for i, σ_0 in enumerate((1, 10, 100)):\n", + " μ_μ, σ_μ, x, density, log_ml, waic, loo = posterior_ml_ic_normal(σ_0, σ_1, y)\n", + " ax[i].plot(x, stats.norm(loc=0, scale=(σ_0**2+σ_1**2)**0.5).pdf(x), lw=2)\n", + " ax[i].plot(x, density, lw=2, color='C4')\n", + " ax[i].plot(0, label=f'log_ml {log_ml:.1f}\\nwaic {waic:.1f}\\nloo {loo:.1f}\\n', alpha=0)\n", + " ax[i].set_title(f'μ_μ={μ_μ:.2f} σ_μ={σ_μ:.2f}')\n", + " ax[i].legend()\n", + "ax[2].set_yticks([])\n", + "\n", + "ax[2].set_xlabel(\"μ\")\n", + "\n", + "#plt.savefig(\"img/chp11/ml_waic_loo.png\")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "a172a527-1572-4fde-8fc9-c63b345b545c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-1.2655121234846454" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "σ_0 = 1\n", + "σ_1 = 1\n", + "y = np.array([0])\n", + "stats.norm.logpdf(loc=0, scale=(σ_0**2 + σ_1**2)**0.5, x=y).sum()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "0ee2d843-352b-4e21-bf76-2cdeee505ce8", + "metadata": {}, + "outputs": [], + "source": [ + "N = 10000\n", + "x, y = np.random.uniform(-1, 1, size=(2, N))\n", + "inside = (x**2 + y**2) <= 1\n", + "pi = inside.sum()*4/N\n", + "error = abs((pi - np.pi) / pi) * 100" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "537dfd77-f109-4d51-ae5e-59114710815e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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QSxabNWsm6dili9UpKiqS0+lUq1atTuuchYWFevbZZ3XNNdeob9++fqmzIbvxvHi1i4kwxq8sYQl8AAAAoK4FJJAlJCQoIiJC+fn5xkzYiXJycpSYmFjrfWbH+/vf/64DBw7owQcf9GepDZYjxK6UQcceKfDF1gPatK/QxIoAAACAhicggcxut2vAgAHyeDzVrkqYkZGhsrIyDR8+/LTO9/3332vu3Lm69tpra31QNM7MPQPaKcxx7I/Aa8t2mFcMAAAA0AAFbK3zkSNHSpLmz59/0r60tDTFxsZqxIgRkiqfKzZhwgSNGjVKGRkZVY4tLS3VE088IUkaO3ZsoMptkOIahen2PgnG+N1V2SooC47nOwAAAAANQcAC2ZAhQ5SUlKS5c+dqwYIFxvYNGzYoNTVVL7zwgnGv2caNGzV79mytWrVKM2fOrHKeF198UdnZ2RoyZIi6desWqHIbrPsu7WB8XVTuUeqqXeYVAwAAADQwAVll8ahJkyapd+/emjp1qqZMmaK4uDg1bdpU06dPV8+ePY3junTpon79+ikzM1NDhw41tv/000+aMWOGJOk3v/lNIEttsC5sE6OB7Ztqxc48SdKrSzN13+AOfl89BgAAAMDJAhrI7Ha7kpOTlZycXOtx4eHhmjVr1knbe/bsqR9//FFer1fh4eGBKrPBu29wByOQpe8v1pdbD+jqxOYmVwUAAABYX8AuWfSHkJAQhYaGEsYC7Nfnt1Z8dJgxfnUpS+ADAAAAdSGoAxnqRqjDrnsHtDPG8zfu045DJSZWBAAAADQMBDJIkn5/SXuF2CvvG/P6pNdZAh8AAAAIOAIZJEkJTSJ0U6+WxvjfK7NU6vKYWBEAAABgfQQyGO6/tKPx9aESl2at3W1iNQAAAID1EchguLRjM53fqrExfmVJpnw+n4kVAQAAANZGIIPBZrPpvsEdjPG6PQVafmQ5fAAAAAD+RyBDFaP6JSgmwmmMX126w7xiAAAAAIsjkKGKyFCH7rq4rTGe++Me7S0oM7EiAAAAwLoIZDjJmEs6yFa5Ar7cXp+mrdhpbkEAAACARRHIcJLOcY10Q/cWxnjq8p2qcHtNrAgAAACwJgIZqnX8Evg5heWat2GvidUAAAAA1kQgQ7Wu6dpcXeMaGeNXlmSaWA0AAABgTQQyVMtut2nscUvgL92Rp7W7D5tXEAAAAGBBBDLUaPRFbdUoNMQYswQ+AAAA4F8EMtSoSYRTd17YxhjPXLNLB4srTKwIAAAAsBYCGWp13+Bji3uUub16a2WWidUAAAAA1kIgQ616tozWlZ1jjfHry3bI4/WZWBEAAABgHQQynNLxS+DvyCvVp5v2mVgNAAAAYB0EMpzSjefFq21MuDF+ZSlL4AMAAAD+QCDDKTlC7Eq5pIMxTttyQJtzC80rCAAAALAIAhlOyz0D2inMceyPy2vLdppYDQAAAGANBDKcluZRYbqtT2tj/O4P2Sosc5tYEQAAAFD/Echw2o5fAr+w3K3U1dkmVgMAAADUfwQynLaL2sZoQLsYY/zq0h3y+VgCHwAAADhbBDKckeNnyTbnFumrbQdMrAYAAACo3whkOCO/vqCVWkSFGuNXlrAEPgAAAHC2CGQ4I2GOEN07sL0xnr9xn3YcKjGxIgAAAKD+IpDhjP1+YHuF2G2SJK9PemM5S+ADAAAAZ4NAhjPWJiZCv+rV0hj/+/udKnV5TKwIAAAAqJ8IZDgr9x+3uMfBEpfeX7vbxGoAAACA+olAhrNyWadm6t0q2hi/sjSTJfABAACAM0Qgw1mx2WxVlsBfu7tAK3bmmVgRAAAAUP8QyHDWRvVNUEyE0xi/unSHecUAAAAA9RCBDGetUZhDv+3f1hjP/WmPcgrKTKwIAAAAqF8IZDgnYwZ1kK1yBXy5PD5NW5FlbkEAAABAPVIvA9nKlSv1yCOPaNSoUdq8ebPZ5TRoXeIa6fpuLYzx1BU75PJ4TawIAAAAqD8cgX6D1atXa9q0acrLy1NBQYEcDoeSkpI0evRohYaGntG5srKyNGHCBBUUFGjcuHEaNGhQgKrGmbj/0o76dHOuJGlvQbk+Wr9Xt/ZJMLkqAAAAIPgFdIZs4cKFGjNmjMaMGaM5c+Zo4cKFGjt2rF566SWlpKTI4zn9hwl//vnn+uUvf6nzzjtPc+bMIYwFkaGJzdUlrpExZnEPAAAA4PQELJBlZWVp/PjxSklJUZ8+fYztN9xwg26++WYtXbpUM2bMOK1zLViwQI888ojuvvtuPfroo3I4Aj6xhzNgt9s0dlAHY7wk85DW7T5sXkEAAABAPRGwQJaamqqysjINGzbspH1JSUmSpHnz5p3yPNu2bdOTTz6pSy65RPfdd5/f64R/jO7fVpHOEGP86rId5hUDAAAA1BMBC2RpaWmKiYlRfHz8Sft69eqlkJAQpaenq6Kiotbz/PWvf1Vpaan++Mc/ynZ0OT8EnZgIp+68qI0xnrlmlw6V1N5bAAAAoKELyLV/hYWFysnJUZcuXardHx4ertjYWOXm5io7O1udO3eu9rjNmzdryZIlSkxMVPfu3QNR6hnx+XynDJCB5HK5qv06WPyuf4KmLt8pSSp1eTV9eaYeuayjyVUFt2DvKc4OfbUeemo99NSa6Kv1BGNPfT6fX88XkECWm1u54l5UVFSNx8TFxSk3N1fFxcU1HvPNN99Iki644AJt375db731lrZv367c3Fy1bNlS1113nW6//XaFhITUeA5/crvdWr9+fZ2816kE63L/F7YI1ercytA6ZXGGrmxcqBA7M5unI1h7inNDX62HnloPPbUm+mo9Vu1pQC5ZLCgokKRaF98ICwuTpFpnnNauXStJWrx4sebOnav/9//+n2bOnKm3335bDodDf/nLX/Twww/7r3Ccs1sSj622uKfYo2V7y02sBgAAAAhuAZkhc7vdklTrsvZ2e2UWjIyMrPGY/fv3S5KuueYajR8/3tjetm1bvfLKKxo6dKgWLVqkpUuXavDgwf4ovVYOh0M9evQI+PvUxOVyGZ8MdO/eXU6n07RaatLjPK/+tf477T5cJkn6dK9NY6/rbXJVwas+9BRnjr5aDz21HnpqTfTVeoKxp5s2bTLyjj8EJJAdfeBzfn5+jceUl1fOnERHR9d4TGFhoSRVG7aioqJ0/fXX6z//+Y+WL19eJ4HMZrOd8cOsA8XpdAZNLccLlTRmUAc9+VnlX5wvth5UZn6FurWo+fJVVArWnuLc0FfroafWQ0+tib5aT7D01N8LDQbkksVmzZpJOnbpYnWKiorkdDrVqlWrGo+JiIiQdOzyxhN16tTplO+DunfPxe0UGnLsj9ZrLIEPAAAAVCsggSwhIUERERHKz883ZsJOlJOTo8TExFrvM2vbtq0kad++fdXuP7rCydEAiODQIjpMt/VpbYzf+SFbhWX+m9YFAAAArCIggcxut2vAgAHyeDzVrkqYkZGhsrIyDR8+vNbzDBgwQJK0devWavdnZmZKqv6SRpjrvsHHlrsvLHfrvdW7TKwGAAAACE4BezD0yJEjJUnz588/aV9aWppiY2M1YsQISZLX69WECRM0atQoZWRkGMclJSUpJiZGn332mcrKyqqco6ysTIsWLdLFF1+s/v37B+rbwFnq3y5GF7eNMcavLs30+zMbAAAAgPouYIFsyJAhSkpK0ty5c7VgwQJj+4YNG5SamqoXXnjBuNRw48aNmj17tlatWqWZM2cax8bExGjSpEk6cOCAHn/8cZWWlkqSiouL9cQTT6hJkyb6xz/+EahvAefovks7GF9vyi3S19sOmlcMAAAAEIQCssriUZMmTVLv3r01depUTZkyRXFxcWratKmmT5+unj17Gsd16dJF/fr1U2ZmpoYOHVrlHFdccYVmz56tKVOmaOjQoYqPj5fdbtc111yjv/3tb0Gx9CWqd8sFrTXuk43aX1z5rLlXlmbqF13jTK4KAAAACB4BDWR2u13JyclKTk6u9bjw8HDNmjWrxv09e/bUG2+84e/yEGBhjhDdO7C9Jn5ZeQ/gJz/naOehErVvVvOz5wAAAICGJGCXLAKSlHJJe4XYK5/V4PVJb6zYaXJFAAAAQPAgkCGg2sRE6Fe9WhrjN1fsVJnLY2JFAAAAQPAgkCHg7hvcwfj6YIlL76/bY14xAAAAQBAhkCHgLu8Uq14to43xK0tYAh8AAACQCGSoAzabrcos2Zrdh/V9Vr5p9QAAAADBgkCGOnFHvzZqEn5sUc9XlmSaWA0AAAAQHAhkqBONwhz67cXtjPHcn/Yop6DMxIoAAAAA8xHIUGfGDupgfO3y+DT9+yzzigEAAACCAIEMdaZLXCNd372FMZ66fKdcHq+JFQEAAADmIpChTt1/3OIeewrKNG99jnnFAAAAACYjkKFOXduthTrHRhrjV5eyuAcAAAAaLgIZ6pTdbtPY42bJvss8pB/3HDavIAAAAMBEBDLUud/2b6dIZ4gxfnXpDvOKAQAAAExEIEOdi4lw6o4L2xjjGWt26VBJhYkVAQAAAOYgkMEU9x132WKpy6u3V2abVwwAAABgEgIZTNG7VWMN6RRrjF9fvkMer8/EigAAAIC6RyCDae6/tIPx9faDJfpsc655xQAAAAAmIJDBNL/s2VJtmoQbY5bABwAAQENDIINpHCF2/f6S9sb48/T92rK/yMSKAAAAgLpFIIOp7h3QXqEhx/4YvrZsh3nFAAAAAHWMQAZTtYgO0619Whvjd37IVlG528SKAAAAgLpDIIPpjl8Cv6DMrfdW7zKvGAAAAKAOEchguovbNVX/tjHG+NWlmfL5WAIfAAAA1kcgQ1A4fpZs474ifZNx0LxiAAAAgDpCIENQuOWC1mreKNQYv7KEJfABAABgfQQyBIVwZ4juGdjOGH/8c46y8kpMrAgAAAAIPAIZgkbKJR0UYrdJkrw+6Y3lO02uCAAAAAgsAhmCRtuYCI3o2dIYv/l9lspcHhMrAgAAAAKLQIagcvziHgeKKzR73R7zigEAAAACjECGoDKkc6x6xkcb41dYAh8AAAAWRiBDULHZbFVmyVbvOqyvth0wryAAAAAggAhkCDp3XNhGsZFOYzxhYTqzZAAAALAkAhmCTlSYQ3+8sosxXr4zT59tzjWxIgAAACAwCGQISvcN6qAWUcceFM0sGQAAAKyIQIag1CjMoT9d1dUYr9l9WP/dkGNiRQAAAID/BX0gKysrU0lJiSoqKuTx8EyqhuT3A9sroUm4Mf7z5+nyepklAwAAgHU4Av0Gq1ev1rRp05SXl6eCggI5HA4lJSVp9OjRCg0NPeXr7733Xq1cubLG/T179tRHH33kz5IRJMKdIXriqq4a+9F6SdKGnELN/WmPbu2TYHJlAAAAgH8ENJAtXLhQEyZM0LRp09SnTx9J0qeffqpx48ZpxYoVmj59ukJCQk55nujoaEVGRla7Ly4uzp8lI8jcdXE7/f3rbdqRVypJevrzdP1f71ZyhAT95C4AAABwSgELZFlZWRo/frweeughI4xJ0g033KAVK1Zo9uzZmjFjhpKTk095rj/+8Y+69dZbA1Uqgliow64nr0nUPXN+lCSl7y/WzLW7lXxRW5MrAwAAAM5dwKYZUlNTVVZWpmHDhp20LykpSZI0b9680zpXTEyMP0tDPZN8YRt1iWtkjJ9N2yKXx2tiRQAAAIB/BCyQpaWlKSYmRvHx8Sft69Wrl0JCQpSenq6KiopTnqumyxXRMDhC7Prz0ERjvP1gid75IdvEigAAAAD/CEggKywsVE5OTo33d4WHhys2NlYej0fZ2af+wdrhcGjRokUaM2aMkpKSdOedd+qVV17RgQMH/F06gtRtfRJ0XnyUMX7uiy0qd7PqJgAAAOq3gNxDlpubK0mKioqq8Zi4uDjl5uaquLj4lOd7/vnntXXr1irbVq5cqffee09vvPGG+vbte24Fnyafz3daM3qB4nK5qv26oXjyF501clblvWTZ+WV6Y+l2jbmkvclVnZuG3lOroq/WQ0+th55aE321nmDsqc/n38cwBSSQFRQUVJ7cUfPpw8LCJOm0Ak7r1q31j3/8Qx07dtSePXs0f/58TZ8+Xfn5+XrwwQf15ZdfntYS+ufK7XZr/fr1AX+f07F582azS6hznX0+dY1xaGu+W5L0XNoWXRSer3CHNVZcbIg9bQjoq/XQU+uhp9ZEX63Hqj0NyE+ybnflD8y1PcjZbq9861PdH/bAAw/o9ddfV/fu3RUWFqaOHTvqwQcf1D//+U9JlbNx3377rZ8qRzCz22xKOb+xMT5Y5tUHW0tMrAgAAAA4NwGZITs6W5Wfn1/jMeXl5ZIqnzFWm4svvrja7VdffbW6du2qrVu3aseOHWdV55lyOBzq0aNHnbxXdVwul/HJQPfu3eV0Ok2rxSy9evn0/vbv9cOuw5KkGVtK9dQv+ysqLODPOA8IempN9NV66Kn10FNroq/WE4w93bRpkzEB5Q8B+Sm2WbNmko5dulidoqIiOZ1OtWrV6qzf52ggq6tVGG02W51cGnk6nE5n0NRS1/5yfXddN/17SdKBEpfeWLlbj1/V1eSqzl1D7qmV0VfroafWQ0+tib5aT7D01Gaz+fV8AblkMSEhQREREcrPzzdmwk6Uk5OjxMTEWu8zO5WjN/YNGDDgrM+B+ueaxOa6tGMzY/ziNxk6XBocN3kCAAAAZyIggcxut2vAgAHyeDzVLoKRkZGhsrIyDR8+vMZz7Ny585T3hm3dulVXXnmlunTpcs41o/6w2Wz6y3XdjHFeqUv/XLzdxIoAAACAsxOw5elGjhwpSZo/f/5J+9LS0hQbG6sRI0ZIkrxeryZMmKBRo0YpIyNDkhQfH6+XX365xmXxFy9eLJfLpWeffTYw3wCC2pDOcbqq67Hn3P1z8XYdLDbvkQQAAADA2QhYIBsyZIiSkpI0d+5cLViwwNi+YcMGpaam6oUXXjDuNdu4caNmz56tVatWaebMmZIqHx59xRVX6A9/+IMyMzON1/t8Pn3xxRd699139d5776lFixaB+hYQ5J699tgsWWG5W//4NsPEagAAAIAzF9Cl6SZNmqTevXtr6tSpmjJliuLi4tS0aVNNnz5dPXv2NI7r0qWL+vXrp8zMTA0dOtTYftttt+m5557TyJEjFR0drY4dOyomJkaXXHKJpk+fbiydj4bpkg7NdEP3Fvp0c+WDyKd8l6mHL+uk+OgwkysDAAAATk9AA5ndbldycrKSk5NrPS48PFyzZs06aXuLFi30r3/9K1DlwQKeua6bEchKXB5N+nqbJif1PMWrAAAAgODAFBPqtQvbxOhXvVoa49eX7dDuw6UmVgQAAACcPgIZ6r2nr+2mo4+DKHd7NfHLbeYWBAAAAJwmAhnqvd6tGuuWC1ob4ze/36mdh0pMrAgAAAA4PQQyWMKfhybKfmSWzOXx6S9fbDW3IAAAAOA0EMhgCd1bROuOfm2M8bursrXtQPXPsAMAAACCBYEMlvHUNYlyHJkm83h9enZRuskVAQAAALUjkMEyOsc10uj+bY3xjLW7tWlfoYkVAQAAALUjkMFSnry6q0JDKv9Y+3zSM4u2mFwRAAAAUDMCGSylXdNI3TuwnTGe8+Me/bjnsIkVAQAAADUjkMFyHr+qq8Idx/5oP/0595IBAAAgOBHIYDmtGodr7OAOxvjjn/fph6x80+oBAAAAakIggyWNv7KLGoWGGOM/f77ZxGoAAACA6hHIYEnNo8L04GUdjfHC9P1amnnIxIoAAACAkxHIYFl/GNJZjcMdxnjCQmbJAAAAEFwIZLCsZpGheuTyTsb464yD+mrrARMrAgAAAKoikMHSHr6sk5pFOo3xhM83y+fzmVgRAAAAcAyBDJbWJMKpcVd0NsbLduTp8/T9JlYEAAAAHEMgg+U9MLijWkSFGuMJC5klAwAAQHAgkMHyGoU5NP4XXYzxql2H9cnP+0ysCAAAAKhEIEODkHJJB7VuHG6M//x5urxeZskAAABgLgIZGoQIZ4gev6qrMf5pb4E++GmviRUBAAAABDI0IHcPaKt2MRHG+OlF6fIwSwYAAAATEcjQYIQ5QvTUNYnGeHNukWau3WViRQAAAGjoCGRoUJIvaqPOsZHG+NlFW+TyeE2sCAAAAA0ZgQwNijPErglDj82SZRws0bursk2sCAAAAA0ZgQwNzsi+bdS9RZQxfi5tq8rdHhMrAgAAQENFIEODE2K36emh3YxxVn6p/v09s2QAAACoewQyNEg3n99K57dqbIyf/3KLSl3MkgEAAKBuEcjQINntNj1z7bFZsr0F5Xpj+Q7zCgIAAECDRCBDg5XUM14XtWlijP/25TYVlbtNrAgAAAANDYEMDZbNZtOz13U3xvuLK/TK0kwTKwIAAEBDQyBDg3Ztt+Ya1KGpMX7h6wwdLnWZWBEAAAAaEgIZGjSbzaa/HDdLllfq0kvfbTexIgAAADQkBDI0eFd2idOVnWON8T8Xb9ehkgoTKwIAAEBDQSADpCr3khWUufWPbzJMrAYAAAANBYEMkDS4YzNd1625MZ6yJFP7i8pNrAgAAAANQb0NZDt27JDLxeIL8J9nrj02S1Zc4dGkr7eZWA0AAAAagoAHstWrV+v3v/+9brnlFl133XUaPny4pk2bpoqKs7tHp7S0VL/5zW907bXXat++fX6uFg1Z/3Yx+mXPeGP82tId2nO4zMSKAAAAYHUBDWQLFy7UmDFjNGbMGM2ZM0cLFy7U2LFj9dJLLyklJUUej+eMzzl58mStWLEiANUCVWfJytxe/fWrrSZWAwAAAKsLWCDLysrS+PHjlZKSoj59+hjbb7jhBt18881aunSpZsyYcUbnXLt2rbZvZ0lyBM75rRvrlgtaG+PpK7KUlVdiYkUAAACwsoAFstTUVJWVlWnYsGEn7UtKSpIkzZs377TPV1FRoUmTJun555/3W41Adf48NFF2W+XXFR6vnvuCWTIAAAAERsACWVpammJiYhQfH3/Svl69eikkJETp6emnfS/Z1KlTdfPNN6tly5b+LhWookd8tEb2TTDGb/+QrYwDxSZWBAAAAKtyBOKkhYWFysnJUZcuXardHx4ertjYWOXm5io7O1udO3eu9XwZGRn66aef9MADDwSi3NPm8/nOejESfzh+VUlWmAysP13ZUbPW7ZHH65PH69PTn2/Wv3/d2+/vQ0+tib5aDz21HnpqTfTVeoKxpz6fz6/nC0ggy83NlSRFRUXVeExcXJxyc3NVXFz7zIPP59PEiRM1YcIEv9Z4Ntxut9avX292GZKkzZs3m12C5Q3vEKGPt1fePzZr3R6NaO1Sh8bOgL0fPbUm+mo99NR66Kk10VfrsWpPA3LJYkFBgSTJ4ag574WFhUnSKWecPvzwQ1144YVq3769/woETsPdvaLkOPI3xOuTpq0vNLcgAAAAWE5AZsjcbrck1bqsvd1e+ZNuZGRkjcfk5+frgw8+UGpqqn8LPEsOh0M9evQw7f1dLpfxyUD37t3ldAZutgZSb0l379uoqd9nS5LSsso08Zcd1LtVtN/eg55aE321HnpqPfTUmuir9QRjTzdt2mTkHX8ISCALDQ2VVBmoalJeXi5Jio6u+YfbyZMna8yYMcb5zGaz2YKmFqfTGTS1WNlTQ7vr3dW7Veb2SpKe/3q7PhrdPyDvRU+tib5aDz21HnpqTfTVeoKlpzabza/nC0gga9asmaRjly5Wp6ioSE6nU61atap2f3p6uj788EOtXLlSf/3rX6s9ZvTo0XI4HBo0aFBQ3GMG62ndJFwpgzropcWVz7/774Ycrd6VrwvbxJhbGAAAACwhIIEsISFBERERys/PV3l5uXG/2PFycnKUmJhY431m8+bNk9vtVmZmZo3vk51deSlZp06d/FM4UI3Hruyiact3qsRVeQnunxema8E9A0yuCgAAAFYQkEU97Ha7BgwYII/HU+2qhBkZGSorK9Pw4cNrPMdjjz2m9PT0an8d9eWXXyo9PV2vvfZaIL4NQJLUIjpMD1zW0Rh/ujlXy3ccMrEiAAAAWEXAHgw9cuRISdL8+fNP2peWlqbY2FiNGDFCkuT1ejVhwgSNGjVKGRkZtZ63qKjI+Nrr9fqvYKAW44Z0VnTYsdncCZ+n13I0AAAAcHoCFsiGDBmipKQkzZ07VwsWLDC2b9iwQampqXrhhReMe802btyo2bNna9WqVZo5c2at583Jyan2ayCQYhuF6pHLj10a++XWA/pm2wETKwIAAIAVBOQesqMmTZqk3r17a+rUqZoyZYri4uLUtGlTTZ8+XT179jSO69Kli/r166fMzEwNHTq02nPdcccdKi0t1a5du4xtv//979W2bVsNGDBATzzxRCC/FUCPXN5JU5ZkKq+08inxEz5P17edY/2+0g4AAAAajoAGMrvdruTkZCUnJ9d6XHh4uGbNmlXrMf/5z3/8WRpwxppEOPWHKzrryc8qn4WxJPOQFm3Zr2u7tTC5MgAAANRXAbtkEbCiBy/tqLhGx55/MWFhunw+n4kVAQAAoD4jkAFnICrMofFXdjHGP2Tna8HGfSZWBAAAgPqMQAacoTGD2qtV42PP1pvwebq8XmbJAAAAcOYIZMAZigx16E+/6GqMf9xToI/W7zWxIgAAANRXBDLgLNw7sJ3axoQb4z9/ni4Ps2QAAAA4QwQy4CyEOUL05NWJxnhTbpHeX7fbxIoAAABQHxHIgLM0un9bdYqNNMbPLNoit8drYkUAAACobwhkwFlyhtg14Zpjs2TbDhQrdfWuWl4BAAAAVEUgA87BqH5t1K15I2P8l7QtqnAzSwYAAIDTQyADzkGI3aanr+1mjHfmlerfK7NMrAgAAAD1CYEMOEe/Pr+1ereKNsbPf7FVpS6PiRUBAACgviCQAefIbrfp6aHHZsn2FJRp6vKdJlYEAACA+oJABvjBiF4t1S+hiTH+21dbVVzuNrEiAAAA1AcEMsAPbDabnr3u2CxZblGFXl22w7yCAAAAUC8QyAA/ub57C13Svqkx/vvX21RQ5jKxIgAAAAQ7AhngJyfOkh0qcenl7zJNrAgAAADBjkAG+NEvusRpSKdYYzz52wzllVSYWBEAAACCGYEM8KMTZ8kOl7n14rfbTawIAAAAwYxABvjZZZ1iNTSxuTH+15Lt2l9UbmJFAAAACFYEMiAAjp8lKyr36O9fZ5hYDQAAAIIVgQwIgIvbNdWN58Ub49eWZWpvQZmJFQEAACAYEciAAHnm2mOzZKUur/761TYTqwEAAEAwIpABAdInoYluPr+VMZ62fKey80tNrAgAAADBhkAGBNCfh3aTzVb5dYXHq+e+2GJuQQAAAAgqBDIggHq2jNbIvgnG+O2V2dp+sNjEigAAABBMCGRAgE24JlEh9sppMrfXp+fStppcEQAAAIIFgQwIsK7No5R8URtjnLo6W+m5RSZWBAAAgGBBIAPqwFNXJ8oZUjlL5vVJz6ZxLxkAAAAIZECd6NAsUndd3M4Yv79utzbsLTCxIgAAAAQDAhlQR564qqvCHJV/5Xw+6elF6SZXBAAAALMRyIA60iYmQr+/pL0x/mh9jtbuZpYMAACgISOQAXXosSu7KNIZYoyf/WKbidUAAADAbAQyoA61bByu+wZ3MMafpe/X+gMV5hUEAAAAUxHIgDr2xys7Kyrs2CzZGz9x2SIAAEBDRSAD6lhcozA9fFknY7xyX4VW55abWBEAAADMQiADTPD/hnRWTITTGE/9qVA+n8/EigAAAGAGAhlggpgIp/4w5Ngs2dr9Ffpy20ETKwIAAIAZHIF+g9WrV2vatGnKy8tTQUGBHA6HkpKSNHr0aIWGhp7y9R6PR3PmzNHHH3+sbdu2yev1qm3btkpKStIdd9yhsLCwQH8LQEA8eGknvbR4uw6WuCRJj/4vXVd0baHI0ID/tQQAAECQCOgM2cKFCzVmzBiNGTNGc+bM0cKFCzV27Fi99NJLSklJkcfjOeU57rvvPj399NPauHGjGjdurIqKCm3evFl///vflZycLJfLFchvAQiY6HCHxg3paIw35hbpgf9uMLEiAAAA1LWABbKsrCyNHz9eKSkp6tOnj7H9hhtu0M0336ylS5dqxowZtZ4jOztbK1eu1J/+9Cf98MMP+uqrr7RmzRrdf//9kqR169bp888/D9S3AATcfZe013nNjt1L9vbKbKWuyjaxIgAAANSlgAWy1NRUlZWVadiwYSftS0pKkiTNmzev1nMsWbJEKSkpGj16tHFpYmhoqB544AFdeeWVkqR9+/b5uXKg7oQ67Prr4KaKdtqMbWM/XK+NOYUmVgUAAIC6ErBAlpaWppiYGMXHx5+0r1evXgoJCVF6eroqKmp+KG7fvn01cuTIave1a9dOknTRRRf5p2DAJK2jHPrzwBhjXOLy6Jb3Vqm43G1eUQAAAKgTAVk9oLCwUDk5OerSpUu1+8PDwxUbG6vc3FxlZ2erc+fO1R7XvXv3are73W4tXbpUt9xyiy644AK/1X0qPp+v1gAZaMffL8e9c9ZwtI9D2kTo/kui9MryyssVN+4rUsoHP+rNm3vJZrPVdgoEIf6uWg89tR56ak301XqCsaf+flRRQAJZbm6uJCkqKqrGY+Li4pSbm6vi4uIzOvehQ4f017/+Vb/4xS/08MMPn0uZZ8ztdmv9+vV1+p412bx5s9klwM9GtXPr2y1OrT9Y+Y/NjLV71MlZoqTOkSZXhnPB31XroafWQ0+tib5aj1V7GpBAVlBQUHlyR82nP3pP2OnOOI0YMUIFBQXKz89XSUmJOnXqJJfLpd///vdq2rTpuRcNmMxht2ni4Ka6Y+F+Ha6o/OTl76vz1aOZU12bOk/xagAAANRHAQlkbnflvS+1LWtvt1fevhYZeepP/71er5588kldeOGFstls+vnnn/XYY4/p7bff1tdff6158+ad1nnOlcPhUI8ePQL+PjVxuVzGJwPdu3eX08kP6fXdiT3t7XTqnZj9+lXqGklSuUf686piLbvvEkWH8Xyy+oK/q9ZDT62HnloTfbWeYOzppk2bjLzjDwH5Ce/oA5/z8/NrPKa8vFySFB0dfcrz2e32Kot39OzZUy+99JJuvPFG7dixQwsXLtRNN910bkWfBpvNdloPs64LTqczaGqBfxzt6S/PT9CjVxbo719vkyRtPVCiBz/ZrP+M7Mv9ZPUQf1eth55aDz21JvpqPcHSU3//PBaQVRabNWsm6dili9UpKiqS0+lUq1atzuo9OnfurISEBEnS3r17z+ocQLB67rpuurRjM2M8a+1uTVux08SKAAAAEAgBCWQJCQmKiIhQfn6+MRN2opycHCUmJtZ6n1ltlzxKUkxMjCSpY8eOZ10rEIwcIXbNuqOf4hod+xTo4Y9/1trdh02sCgAAAP4WkEBmt9s1YMAAeTyealclzMjIUFlZmYYPH17jOXbu3Kknnniixv0ej0dZWVlq2bKlrr76ar/UDQSThCYRem9kXx2dFS93e3Xre6tVUBYcS74CAADg3AXswdBHH+g8f/78k/alpaUpNjZWI0aMkFS5aMeECRM0atQoZWRkSJLat2+vNWvW1Li85eeff66SkhJNmjQpKK4lBQLh2m4t9KdfdDXG2w4U6945P/r9+RcAAAAwR8AC2ZAhQ5SUlKS5c+dqwYIFxvYNGzYoNTVVL7zwgnGv2caNGzV79mytWrVKM2fONI7t16+fxowZo6VLl1Y599KlS/Xmm2/qzTff1MCBAwP1LQBB4emhiRrSKdYYz/1pr15btsO8ggAAAOA3AV1He9KkSerdu7emTp2qKVOmKC4uTk2bNtX06dPVs2dP47guXbqoX79+yszM1NChQ43tI0eOVElJiR577DHZbDZ169ZNMTExuvDCC/Wf//ynTpa6B8zmCLFr5h391Hfyt8otqnxu3x8+2aiB7ZvqwjYx5hYHAACAcxLQQGa325WcnKzk5ORajwsPD9esWbNO2n7++efrX//6V6DKA+qNVo3DNWNUPw2dtkI+n1Th8eqW1NVa/cjliokw/3kcAAAAODsBu2QRgH9d1bW5JlyTaIwzD5Xo7tnruJ8MAACgHiOQAfXIk1cn6uquccZ43oYcvfxdpokVAQAA4FwQyIB6JMRu03sj+6lldJix7dEFG/X9zjwTqwIAAMDZIpAB9Ux8dJhm3dFP9iPPJ3N7fbr1vdU6VFJhbmEAAAA4YwQyoB4a0jlOz1zbzRhn5Zfqt+9zPxkAAEB9QyAD6qk//aKrru3W3BjP37hPL3673cSKAAAAcKYIZEA9ZbfblHp7XyU0CTe2/enTTVq245CJVQEAAOBMEMiAeqx5VJjev+NChRy5oczj9em291brQHG5yZUBAADgdBDIgHpucMdmev767sZ41+EyJc9cK6+X+8kAAACCHYEMsIBxQzprWI8Wxnhh+n5N+nqbiRUBAADgdBDIAAuw221657a+ahtz7H6ypxZu1uKMgyZWBQAAgFMhkAEWEdsoVLPvvEiOI/eTeX3S7TNWK7eQ+8kAAACCFYEMsJCB7Zvqb8N6GOO9BeW6c9YaebifDAAAICgRyACLeeTyTvplz3hjnLblgCZ+udXEigAAAFATAhlgMTabTW/d2kcdmkYY255ZlK6vtx0wsSoAAABUh0AGWFDTyMr7yZwhx+4nGzljjXIKykyuDAAAAMcjkAEW1b9djP5xY09jvK+wXKNmcD8ZAABAMCGQARZ2/+AOuvn8Vsb464yDemZRuokVAQAA4HgEMsDCbDabpv/6AnWOjTS2Pf/lVi1KzzWxKgAAABxFIAMsrkmEU7PvvFChIZV/3X0+6c6Za7XnMPeTAQAAmI1ABjQA/drE6J+/PHY/2f7iCt3+n9Vye7wmVgUAAAACGdBApFzSXrf2aW2Mv8s8pAmfcz8ZAACAmQhkQANhs9k07eYLlNi8kbHtb19t02eb9plYFQAAQMNGIAMakOhwh+bceZHCHcf+6ifPWqvs/FITqwIAAGi4CGRAA3N+68b61696GeODJS7d9t5qubifDAAAoM4RyIAG6O6L2+mOfgnGePnOPD3+6WYTKwIAAGiYCGRAA2Sz2fTa/52v7i2ijG0vfpuh+T/nmFgVAABAw0MgAxqoqDCH5tx5oSKcx/4ZGP3+Ou08VGJiVQAAAA0LgQxowHq1aqxXbzrfGOeVunTre6tV4eZ+MgAAgLpAIAMauNH922p0/7bGeGV2vsb/b6OJFQEAADQcBDIAeuVXvdSrZbQxfvm7TM1bv9fEigAAABoGAhkARYY6NCf5QjUKDTG23TV7nbYfLDaxKgAAAOsjkAGQJHVvEa03bj52P9nhMrdufW+1yt0eE6sCAACwNgIZAMOofm10z4B2xnj1rsP6wyfcTwYAABAoBDIAVbw8opcuaN3YGL+2bIfmrNtjYkUAAADWRSADUEWEM0Sz77xQUWHH7ie7d+6P2rq/yMSqAAAArMkR6DdYvXq1pk2bpry8PBUUFMjhcCgpKUmjR49WaGjoKV+fkZGht956SytWrFBubq4aNWqk8847T7fffruuueaaQJcPNEiJzaM0/dcX6Pb/rJEkFZZX3k+27IFLFe4MOcWrAQAAcLoCOkO2cOFCjRkzRmPGjNGcOXO0cOFCjR07Vi+99JJSUlLk8dS+WMDy5cv1f//3f/rggw9UUlKi5s2bq6CgQEuXLtX999+vf/zjH4EsH2jQbu2ToDGDOhjjdXsK9PDHP5tXEAAAgAUFLJBlZWVp/PjxSklJUZ8+fYztN9xwg26++WYtXbpUM2bMqPUcixcvVtu2bfXf//5Xy5cv11dffaXFixfr6quvliRNnz5dGzZsCNS3ADR4k5POU7+EJsZ42oqdmrV2t4kVAQAAWEvAAllqaqrKyso0bNiwk/YlJSVJkubNm1frOfLy8jRu3Dj16NHD2BYXF6fJkyerdevWkqS0tDQ/Vg3geGGOyvvJGocfu7r59x/8qPRc7icDAADwh4AFsrS0NMXExCg+Pv6kfb169VJISIjS09NVUVFRc3F2uwYNGnTS9rCwMF1xxRWSpIKCAr/VDOBkneMa6d+3XGCMi8o9uuW9VSqpcJtYFQAAgDUEJJAVFhYqJydHcXFx1e4PDw9XbGysPB6PsrOzazzPxIkT5XQ6q91ns9kkSe3btz/3ggHU6v/Ob60HLu1ojNfvLdQD/+VyYQAAgHMVkFUWc3NzJUlRUVE1HhMXF6fc3FwVFxef1Xts3LhRDodD119//Vm9/mz4fL5aZ/QCzeVyVfs16q/61NPnh3bR8h0HtWpX5az02yuzNbhdE93RL8HkyoJPfeorTg89tR56ak301XqCsac+n8+v5wtIIDt6GaHDUfPpw8LCJOmsAs6mTZu0bt063XXXXdVeEhkobrdb69evr7P3q83mzZvNLgF+Vh96+lTfcN2xr1CFrsp/iO6f97OiS/apU5PqZ7JRP/qKM0NPrYeeWhN9tR6r9jQglyy63ZX3ltS2rL3dXvnWkZGRZ3Rul8ulp556Sv3799cjjzxy9kUCOGOtoxz688AYY1zm8emxJXkqdXvNKwoAAKAeC8gM2dEHPufn59d4THl5uSQpOjr6jM49YcIEeb1evfbaazXeXxYoDoejyoqPdc3lchmfDHTv3r3Ov3/4X33sae/e0i5ful5askOSlFng1tRtdr15cy/j3s6Grj72FbWjp9ZDT62JvlpPMPZ006ZNxgSUPwQkkDVr1kxS7SsgFhUVyel0qlWrVqd93hdeeEHbtm3TO++8c8ZBzh9sNpsRNs3mdDqDphb4R33q6aQbe+r77MNavjNPkjRj7R5d2bW57rq4ncmVBZ/61FecHnpqPfTUmuir9QRLT/39AXRALllMSEhQRESE8vPzjZmwE+Xk5CgxMbHW+8yON2XKFP344496++231bhxY3+WC+AMOUPsev/OC9Us8tinVPd/tF7r9/IYCgAAgDMRkEBmt9s1YMAAeTyeahfByMjIUFlZmYYPH35a55syZYrWrVunN998s9aVGwHUnbYxEUq9va8xLnN7dUvqKhWW8XwyAACA0xWwB0OPHDlSkjR//vyT9qWlpSk2NlYjRoyQJHm9Xk2YMEGjRo1SRkZGlWOPzoy9/vrrCg8PP+lcPp/Pr9dwAjh9N/SI16NXdjHG6fuLlfLhT35fDhYAAMCqAnIPmSQNGTJESUlJmjt3rvr372/Mhm3YsEGpqal64YUXjHvNNm7cqNmzZ0uSZs6cqaeeekqS9PLLL+u1115TTEyMrrzyyirn9/l8Ki0tVWlpqe677z498MADgfpWANTiueu6admOQ1qSeUiSNGvtbl3eqZl+f0kHcwsDAACoBwIWyCRp0qRJ6t27t6ZOnaopU6YoLi5OTZs21fTp09WzZ0/juC5duqhfv37KzMzU0KFDJUmLFi3Sa6+9Jqn21RolMUMGmMgRYtesO/qp7+TFOlBc+VzBhz/+WRe3a6q+CU1Mrg4AACC4BTSQ2e12JScnKzk5udbjwsPDNWvWrCrbhg4dqvT09FO+R0VFBUttAyZLaBKh/4zsq+vf/F4+n1Tu9urW91Zr1cOXqXG4+cvTAgAABKuA3UNWV0JDQ4PieQRAQze0Wws9flVXY7ztQLHunfMj95MBAADUot4HMgDB4+mh3XRF51hjPPenvXpt2Q7zCgIAAAhyBDIAfhNit2nGqH6Kjw4ztv3hk41avSvfvKIAAACCGIEMgF+1ahyu/4zsq6O3dlZ4vLoldbXyS13mFgYAABCECGQA/O6qrs014ZpEY5x5qER3z17H/WQAAAAnIJABCIgnr07U1V3jjPG8DTl6+btMEysCAAAIPgQyAAERYrfpvZH91PK4+8keXbBR3+/MM7EqAACA4EIgAxAw8dFhmnVHP9mP3E/m9vp063urlVNQZm5hAAAAQYJABiCghnSO07PXdTfGWfmluuil77Qk86CJVQEAAAQHAhmAgHvsyi66rltzY7ynoExXvr5c//gmg4U+AABAg0YgAxBwdrtN7995oUb0amls83h9enTBRv3fu6tYEh8AADRYBDIAdaJxuFMf/uYivTD8PIUcvalM0n835Kj/S4u1bvdhE6sDAAAwB4EMQJ2x2Wz6wxWd9VXKJWrV+NjqixkHS3TJlCX69/dZXMIIAAAaFAIZgDp3WadYrXlkiH7R5dhzysrdXt0790fdPftHlVS4TawOAACg7hDIAJgiPjpMn/9uoJ64umuV7e+sytYlU5Zoy/4ikyoDAACoOwQyAKYJsdv0l+u6a8HdF6tphNPYvn5vofq/9J0++HGPidUBAAAEHoEMgOlu6BGvNY9crv5tY4xtheVu3fLeaj3y8QZVuL3mFQcAABBABDIAQaF9s0gtvm+Qxg7qUGX7y99l6srXlyk7v9ScwgAAAAKIQAYgaIQ5QvTKTb01Y1Q/NQoNMbYv35mnC/+5WIvSc02sDgAAwP8IZACCzu19E7Tyoct0XnyUse1AcYWuf/N7PbMoXR4vS+MDAABrIJABCEo94qP1/YOXaVS/BGObzyc9s2iLhr35vfYXlZtYHQAAgH8QyAAErUZhDqXe3lev3dRboSHH/rlatGW/LvznYi3fccjE6gAAAM4dgQxAULPZbEoZ1EFL7h+sDk0jjO27DpdpyGvL9PJ32+XzcQkjAAConwhkAOqFi9rGaNUjl2t4j3hjm9vr0yMf/6xb31utgjKXidUBAACcHQIZgHqjWWSo/vvb/pp4Q3fZbce2f/DTXvV/6Tut31tgXnEAAABngUAGoF6x22167Bdd9cXvL1F8dJixfeuBYg3813d694dsE6sDAAA4MwQyAPXSFV3itOaRy3V5p2bGtlKXV7+dvU73zv1RpS6PidUBAACcHgIZgHqrVeNwffH7S/TolV2qbP/391kaPGWJMg4Um1QZAADA6SGQAajXHCF2/W1YD/33t/0VE+E0tq/bU6CLXlqs/27Ya2J1AAAAtSOQAbCEpJ4tterhy9QvoYmx7XCZWze9s0p/nL9RLo/XxOoAAACqRyADYBmdYhtpyf2D9buB7atsf/HbDF31xnLtOVxmUmUAAADVI5ABsJRwZ4jeuPl8vXt7H0U4j/0TtyTzkPr981t9uXW/idUBAABURSADYEl3XthW3z94mbo1b2Rsyy2q0LXTVuj5L7bI6/WZWB0AAEAlAhkAy+rVqrFWPnS5brmgtbHN65OeWpiuG99aqYPFFSZWBwAAQCADYHHR4Q7NuqOf/jWil5whNmP7Z5tzdeE/F2tlVp6J1QEAgIaOQAbA8mw2m+6/tKMWjx2stjHhxvas/FJd9upSvbo0Uz4flzACAIC6Vy8DWVZWltklAKiHBrRvqjWPDNF13Zob21wenx6Yt0GjZqxRUbnbxOoAAEBD5Aj0G6xevVrTpk1TXl6eCgoK5HA4lJSUpNGjRys0NPS0z1NcXKz58+drxowZioiI0Jw5cwJYNQCrim0UqgV3D9DzX27V04vSdXRi7P11e7RuT4HmJl+kni2jzS0SAAA0GAENZAsXLtSECRM0bdo09enTR5L06aefaty4cVqxYoWmT5+ukJCQGl/v8Xi0bNkyffbZZ1q5cqVCQkK0Y8cOXXDBBYEsG4DF2e02PXVNoi5p31SjZqzR/iOLe2zOLdKAl7/T1F+fr1H92phcJQAAaAgCdsliVlaWxo8fr5SUFCOMSdINN9ygm2++WUuXLtWMGTNOeY6///3vuuiii/Tpp59q+PDhgSoXQAN0dWJzrfl/l2twh6bGthKXR3fOXKsxH/6kMpfHxOoAAEBDELBAlpqaqrKyMg0bNuykfUlJSZKkefPm1XqOjh07av78+brpppvO6PJGADhdCU0i9NWYQXrk8k5Vtk9dvlOXvbpUmQdLTKoMAAA0BAELZGlpaYqJiVF8fPxJ+3r16qWQkBClp6erooLnAAEwlzPErheTeuqD31ykxuHHruReveuwLnxpseb/nGNidQAAwMoCcg9ZYWGhcnJy1KVLl2r3h4eHKzY2Vrm5ucrOzlbnzp0DUYbf+Xw+UwOky+Wq9mvUX/Q0uAzvFqvl9w3U7TN/1E97CyVJ+aUu/fLtHzRuSEc9fXUXOUJO/TkWfbUeemo99NSa6Kv1BGNP/f2onIAEstzcXElSVFRUjcfExcUpNzdXxcXFgSghINxut9avX292GZKkzZs3m10C/IyeBo9XL43SC6s9+mT7scsV//Ftpr7atFvPD2qquIiaFyM6EX21HnpqPfTUmuir9Vi1pwG5ZLGgoECS5HDUnPfCwsIkiUsWAQSdcIdNTw2I0VMDYhR2XPZak1uhOxbu1+rccvOKAwAAlhKQGTK3u/Lhqh5PzSuU2e2VWTAyMjIQJQSEw+FQjx49THt/l8tlfDLQvXt3OZ1O02qBf9DT4Na7t3TjxQW6feaPyjiyuMfBMq/GfnVQzw7tqv93WUfZ7baTXkdfrYeeWg89tSb6aj3B2NNNmzYZeccfAhLIjq6ImJ+fX+Mx5eWVnzBHR9efB7DabLagWe3R6XQGTS3wD3oanC5qH6dVD1+uu+es00frKxf38PqkJz/fqu+zC/TObX3UNLLmvtFX66Gn1kNPrYm+Wk+w9NRmO/nD2HMRkEsWmzVrJunYpYvVKSoqktPpVKtWrQJRAgD4TZMIp+YmX6QXk86T47gZsfkb9+nCfy7W6l355hUHAADqtYAEsoSEBEVERCg/P9+YCTtRTk6OEhMTa73PDACChc1m0yOXd9Y3YwcpoUm4sX1HXqkGT1mqqct3+H3VJQAAYH0BCWR2u10DBgyQx+OpdlXCjIwMlZWVafjw4YF4ewAImEEdmmn1w5fr6q5xxrYKj1djPlyv38xaq+Jy/11TDgAArC9gD4YeOXKkJGn+/Pkn7UtLS1NsbKxGjBghSfJ6vZowYYJGjRqljIyMGs9Z2yIhAFBXWkSH6bN7B+qpaxJ1/GXk/1mzWwP/tUTpuUXmFQcAAOqVgAWyIUOGKCkpSXPnztWCBQuM7Rs2bFBqaqpeeOEF416zjRs3avbs2Vq1apVmzpxZ4zn3798vSTp8+LC8Xm+gSgeAUwqx2/TMtd30v7sHKDby2IpPP+8r1ODXVmjRzlITqwMAAPVFQG/gmjRpknr37q2pU6dqypQpiouLU9OmTTV9+nT17NnTOK5Lly7q16+fMjMzNXTo0Crn+Oabb/Tqq6+qtLRUW7dulSTt2LFDV111lWJjY3XHHXcYM20AUNeu695Cqx+5XLe+t1rfZ+VLkooqPHpiWZ6W7S3Ts80L1bddrLlFAgCAoBXQQGa325WcnKzk5ORajwsPD9esWbOq3XfFFVfoiiuuCEB1AOAf7ZpG6tuxg/XHBRs1ZUmmsf1/maX637+W6bKOzTRmUAfd1LuVQh0BuzABAADUQyxxCAB+EOqw6+URvTS4QzPdM2ediiqO3fP6XeYhfZd5SPHRYbr74nb63cB2atc00sRqAQBAsOCjWgDwo1v6tNb3D1yiX3aKVFhI1QdH7iss18Qvt6rTxC/1q7dXalF6rrxelsoHAKAhY4YMAPysc2wjPTkgRg/2baw1ZU007ftd2nqg2Njv9Ukf/7xPH/+8T13iGinlkvYa3b+tmkWGmlg1AAAwAzNkABAgjUPtemBwB2169Eot+t1A/apXS9mrTppp24FijZu/UW2eTdNds9dpVXa+KbUCAABzMEMGAAFmt9t0dWJzXZ3YXNn5pZq+Yqemf5+lfYXlxjFlbq/e+SFb7/yQrf5tYzRmUAfd2qe1IpwhJlYOAAACjRkyAKhDbWMi9Ox13bXziav1/h0Xakink5fE/yE7X3fNXqc2z6Zp3Pyfte24yx0BAIC1EMgAwAShDrtu6dNaX48dpPXjrtDYQR0UHVb1ooW8Upcmf7tdiX/7StdNW6GPN+TI7fGaVDEAAAgEAhkAmKxny2i9clNv7XrqGr12U2/1bhV90jGLtuzXr975QZ3/+qWe/2JLlcsdAQBA/UUgA4AgER3uUMqgDlr3/4Zo8X2DNLJvgpwnLJ2fnV+mpxamq91zaRr5n9X6bvtB+XwsnQ8AQH3Foh4AEGRsNpsu7RirSzvG6sWknnprZZamLt+prPxS4xiXx6f31+3R++v2qFfLaI0Z1EF39Guj6HD+WQcAoD5hhgwAglh8dJj+dFVXZTx+lT7+bX9d1635ScdsyCnUfR+tV8JfFum+j9Zrw94CEyoFAABng49SAaAeCLHbdGPPlrqxZ0ttO1Csqct36u0fsnSoxGUcU1Tu0evLduj1ZTt0eadmGjOog37Vq5VCHXz2BgBAsCKQAUA90yWukV648Tw9e103zVm3R68v26GVJzxQevH2Q1q8/ZDio8N0z4B2+t3A9mobE2FOwQAAoEZ8bAoA9VSEM0S/6d9WKx66TCsfuky/vbitwk+YDdtXWK7nv9iqjs9/oV+9vVKL0nPl9bIICAAAwYJABgAWcFHbGP37lj7aPeEaTU7qqa5xjars9/qkj3/ep+umf6/uf/9ak7/N0KGSCpOqBQAARxHIAMBCmkaG6uHLO2nTo1dq0e8G6le9WspedeV8bTtQrHHzN6rNs2m6a/Y6rTrhckcAAFB3uIcMACzIbrfp6sTmujqxubLzSzV9xU5N/z6rygOly9xevfNDtt75IVv928ZozKAOurVPa0U4Q0ysHACAhoUZMgCwuLYxEXr2uu7a+cTVev+OCzWkU+xJx/yQna+7Zq9Tm2fTNG7+z9p2oNiESgEAaHgIZADQQIQ67LqlT2t9PXaQ1o+7QmMHdVB0WNULJfJKXZr87XYl/u0rXT99hT75OUceFgEBACBgCGQA0AD1bBmtV27qrV1PXaPXbuqt3q2iTzrm8/T9GvH2D+o88UtN/HJrlcsdAQCAfxDIAKABiw53KGVQB637f0O0+L5Bur1vgpwhVVcBycov1ZOfbVa759I0asYafbf9oHw+Zs0AAPAHFvUAAMhms+nSjrG6tGOsJif11L9XZmna8p3Kyi81jnF5fJq1drdmrd2t3q2iNeaSDhrVr42iw/lfCQAAZ4sZMgBAFfHRYXr8qq7KePwqffzb/rquW/OTjlm/t1BjP1qvNn9J09gPf9JH6/cq82AJM2cAAJwhPtYEAFQrxG7TjT1b6saeLbXtQLGmLt+pt3/I0qESl3FMYblbbyzfqTeW75QkxUQ41ad1Y/VJaKK+CY3Vt3UTdW8RJUcIn/8BAFAdAhkA4JS6xDXSCzeep2ev66Y56/bo9WU7tLKaB0rnl7r0TcZBfZNx0NgW7rCrd6vG6nMkoPVNaKLeraIVGcr/ggAA4P+GAIDTFuEM0W/6t9Vv+rfVqux8vbF8pxal52rX4bIaX1Pm9uqH7Hz9cFyAs9uk7i2i1Dehifq0blIZ1hKaqFlkaB18FwAABA8CGQDgrFzUNkZvto2RJO0vKte6PQVau/uw1u0+rLW7D2vLgWLVdEuZ1ydt3FekjfuKNGPNbmN7u5gI9U04eslj5a82TcJls9mqPxEAAPUcgQwAcM6aR4XpmsTmuibx2AIgReVu/bS3MqSt3V2gdbsPa0NOoSo83hrPk5Vfqqz8Un388z5jW2yks3ImzQhpjdU1LkohdkIaAKD+I5ABAAIiKsyhQR2aaVCHZsY2l8erTfuKKkPansrZtHV7ClRQ5q7xPAdLXPpi6wF9sfWAsS3SGaILjl88JKGJerWMVpgjJKDfEwAA/kYgAwDUGWeIXee3bqzzWzfWb9RWkuT1+pR5qOS4kFY5q5ZTWF7jeUpcHi3fmaflO/OMbQ67TefFRxuXPPZp3Vh9WjdRkwhnwL8vAADOFoEMAGAqu92mznGN1DmukW6+oLWxPaeg7EhIKzDuS8s4WFLjedxen37aW6Cf9hbo3VW7jO2dYiPV97iFQ/omNFGrxuEB/Z4AADhdBDIAQFBq2Thc1zcO1/U94o1th0td+nFPgXG549rdBdq4r1Bub80PpN5+sETbD5bow/V7jW3x0WHq27rq4iGdmkXKzn1pAIA6RiADANQbTSKcurxzrC7vHGtsK3d79HNOodYeudRx3Z7D+nFPgYorPDWeZ19huRam79fC9P3Gtugwx3EPta68N+28+Gg5eag1ACCACGQAgHotzBGifm1i1K9NjLHN4/Vp24HiIys8Voa0tbsLdKC4osbzFJa79V3mIX2XecjYFhpiV6+W0Tq/VZSa+4rVqYlDzvgitWkWpaYRTpbjBwCcMwIZAMByQuw2dWsRpW4tonRb3wRJks/n0+7DZceW4d9TGdZ25pXWeJ4Kj1drdh/Wmt2Hj238aqkkyRliU4uoMMVHhSk++rhfUSf8Hh2qZhGhXA4JAKgWgQwA0CDYbDa1iYlQm5gI3dizpbH9UEmFsbLj0ZC2ObdItdyWJklyeSoD3u7DZad8b4fdpuZRoVXCWovoMLWsJsTFNgrlGWsA0IAQyAAADVqzyFD9omucftE1zthWUuHWhpxCYzZt7a58/bT3sMprvi2tVm6vT3sLyrW3oOal/I+y2yoftF0Z0kKN8BYfFaaWjauGt7hGoXJwjxsA1GsBD2SrV6/WtGnTlJeXp4KCAjkcDiUlJWn06NEKDQ09rXPs2bNHU6ZM0ZYtW+T1enX48GFdccUVSklJUYsWLQL8HQAAGprIUIcubtdUF7drKkmqqKjQ2h9/Ul6ZV83adtKhMq/2FZZrX1G59hWWK/fI70fH+4sr5DvFDFtNvL7KRUf2FZZLe2s/1maT4iJDq1wu2aLKjFuoWjYOV3xUmJpHhbJACQAEoYAGsoULF2rChAmaNm2a+vTpI0n69NNPNW7cOK1YsULTp09XSEhIrefYsWOHbrvtNj344IOaOHGibDab0tPTdc899ygtLU0fffSRmjdvHshvAwCAyssOI0PUu3XjU36g6PZ4daC4wgholb9XVBvecovKT3l5ZE18Pml/cYX2F1doQ07hKY+PjXRWuUSyRTX3vLWMDlOLqDCFOghvAFAXAhbIsrKyNH78eD300ENGGJOkG264QStWrNDs2bM1Y8YMJScn13gOr9ersWPHqk+fPho5cqSxvVu3bho/frz+8Ic/6JlnntErr7wSqG8DAIAz5gixq2XjcLU8jQdQe70+HSypDGs5xwW1k8NbhXKLymt95tqpHCxx6WCJSxv3FZ3y2HCHXeHOkMrfj/s64ui2434Pq7LdrnDHsX0RJ4yPHlN5fPWv4R46AA1JwAJZamqqysrKNGzYsJP2JSUlafbs2Zo3b16tgezLL79URkaGxowZc9K+oUOHKjw8XF9//bXy8vLUtGlTv9YPAEBdsNttah4VpuZRYerVqvZjvV6f8kpdVWbYjg9xuccHuqJyuTxnH97K3F6Vub1n/fpz4QyxnRTWTgp8xna7wo4bVw18VY8Nd9oVceT3EJ9XOwvcCg2RYgvKFBnmkyPEphCbTQ67TY4Qmxx2u+w28XgDAAEVsECWlpammJgYxcfHn7SvV69eCgkJUXp6uioqKmq89GPRokWSpMTExJP2hYaGqkePHlq7dq02bdqkQYMG+fcbAAAgyNjtNsU2ClVso1Cdp+haj/X5fMovdR0341ZRJcSdGN7KTQpf1XF5fHJ53Co89Roo/vFJbq27Q+xHQtqRX8fG9hPGthNC3ZH9tqMB78Rz2I2xvco57AqxqXL/kddVPUc173tiXSeFy8qxzSbZZJPdfuT3I4HTJsl+ZH/12yrHxtfVbVPln9GTth193yqvOfLeRg3VbTt2LkIxrCwggaywsFA5OTnq0qVLtfvDw8MVGxur3NxcZWdnq3PnztUet2XLFkmq8R6xhIQErV27Vjt37qyTQObz+VRRUfNDRQPN5XJV+zXqL3pqTfTVeuprTxs5pE4xYeoUE1brcT6fTwXlbuUWVWhfYYX2F5eruMKjUpdX5W6vytweY8as3O1VqatyXO7yHtl+ZL/rhGOP7C91e85pts5sHq9PHq9PdZUPUb2qQbFqgDOCpCSf1yubTQr5b2XQrnxFpaO57vh4d3zYs51w3ElfHzmi6jaddLDt5E0nnP/k9zzr+qpWoBOz64lR9uT9p3h9Lec7MSif83tV83qfz6fS0jI1CbPrzxH7dUUX89eO8J3tqk01CEggy82t/AsQFRVV4zFxcXHKzc1VcXFxjcfs37+/1vPExVUuUVxUdOpr4f3B7XZr/fr1dfJep7J582azS4Cf0VNroq/WY/WeNjnyS84jv2plP/Lr1D9OeLw+ubw+lXukCo9P5V6fyj0+VRz5dXR7hdenMnfl7xUeHTumlu3l7srzVRw993HbK468J+o/r0+qunzpqX4odgewGpjhrtk/6uOkk6++q+8CEsgKCgoqT+6o+fRhYZWf1tU243Sq8xw9R336tBIAgIYo5MgldeEmPAHV5/PJ5T0W1ozAdiTAeXw+eXySx6vKr72qHBvbffL6JPeRr419xx/n1ZFjfMZ5vL7K/e4jr/Eeeb3bd9z+I8e6T3jN0eO8J77nKer0HHk9YEVNw625+mtA/ll0uys/kfB4av5Iym6v/A8aGRl5yvO43e5q7zM7nXP4k8PhUI8ePerkvarjcrmMT2a7d+8up/OUH10iyNFTa6Kv1kNPrcfKPfUdCXZur09ur1cer+T2euX2+uTzVc4r+XyS1+eTT0d+P7Ld+PrIPuO4444/1WtPOq6G1/qqfa3kk6/Ka2s9t4685sjXLpdbe3NyJEkt41vKftzjlY5eZlZlju24ge/InqrbTj7Wd9zW6o6t7pxVX1+1V7W//uRja9p/4vmq369T7D/915/pa0/c4DthQ021eTxeHTp0UI1D7XromvPVPrbmK/DqyqZNm4yc4g8BCWRHw1N+fn6Nx5SXV16JHR1d803JoaGhKi8v1+HDh6u9j+zoOWq7NNKfbDbbaT/MOtCcTmfQ1AL/oKfWRF+th55aDz21joqKCq1fX/lMvt69O9BXC6jsaeUtQ+1jo4Kip/5eZCYg837NmjWTdOySw+oUFRXJ6XSqVaua1/iNjY2t9TxH7z9r37792ZYKAAAAAKYJSCBLSEhQRESE8vPzjVmsE+Xk5CgxMbHW+8w6depkHFudvXv3yuFwVLssPgAAAAAEu4AEMrvdrgEDBsjj8VS7KmFGRobKyso0fPjwWs9zdCn7H3/8sdr9Gzdu1GWXXaYmTZqce9EAAAAAUMcCtlTJyJEjJUnz588/aV9aWppiY2M1YsQISZLX69WECRM0atQoZWRkGMeNGDFCkZGR+t///nfSjYJr1qzRoUOHdNdddwXqWwAAAACAgApYIBsyZIiSkpI0d+5cLViwwNi+YcMGpaam6oUXXjDuNdu4caNmz56tVatWaebMmcaxsbGxevzxx7Vt2zZNnDjRWCL/0KFDeu6553Tffffp4osvDtS3AAAAAAABFdCngUyaNEm9e/fW1KlTNWXKFMXFxalp06aaPn26evbsaRzXpUsX9evXT5mZmRo6dGiVc/z6179WixYtNH36dF133XWKj49XWFiY7r33Xl1//fWBLB8AAAAAAiqggcxutys5OVnJycm1HhceHq5Zs2bVuH/IkCEaMmSIv8sDAAAAAFNZ83HXAAAAAFAPEMgAAAAAwCQEMgAAAAAwCYEMAAAAAExCIAMAAAAAkxDIAAAAAMAkBDIAAAAAMAmBDAAAAABMQiADAAAAAJMQyAAAAADAJDafz+czu4hgt2bNGh39z+R0Ok2rw+fzye12S5IcDodsNptptcA/6Kk10VfroafWQ0+tib5aTzD21OVySZJsNpv69et3zudznPMZGoDjM+vRBpjt6B9MWAc9tSb6aj301HroqTXRV+sJtp76a16LQHYa7Ha7vF6vbDabHA7+kwEAAAANldvtls/nk93un7u/uGQRAAAAAEzCoh4AAAAAYBICGQAAAACYhEAGAAAAACYhkAEAAACASQhkAAAAAGASAhkAAAAAmIRABgAAAAAmIZABAAAAgEkIZAAAAABgEgIZAAAAAJiEQAYAAAAAJiGQAQAAAIBJCGQAAAAAYBICGQAAAACYhEAGAAAAACYhkAEAAACASQhkAAAAAGASAhkAAAAAmIRABgAAAAAmIZABAAAAgEkIZECQ8Pl8ysjIMLsM+JHH49F///tf3X333XrwwQd1+PBhs0sCGrSKigrl5OSYXQb8iJ5a09n0dceOHXK5XAGqKLBsPp/PZ3YRqN3SpUuVmpqqjRs3Ki8vT82aNVP//v11zz33qEePHmaXBz9IT0/XAw88ILfbra+++srscuAHy5Yt09NPP60ePXrooYceUqdOncwuCefgk08+0dy5c1VUVCSbzabCwkINHjxYKSkpatmypdnl4RRycnI0e/ZszZkzR7/61a80bty4ao/bs2ePpkyZoi1btsjr9erw4cO64oorlJKSohYtWtRx1ajN6fQ0IyNDb731llasWKHc3Fw1atRI5513nm6//XZdc801JlSNUzndv6vHKy0tVUpKilasWKEvv/xSbdq0qYNK/cthdgGo3dSpUzV58mTZbDa1bNlSMTEx2rdvnxYsWKCFCxdqypQp+sUvfmF2mTgHHo9Hf/rTn7Rz504lJCSYXQ784MUXX1Rqaqr++te/6oYbbjC7HJwDn8+nRx99VGvXrtWrr76qbt26SZJ2796tMWPG6Ne//rU++ugjNW/e3ORKcaKioiJ99dVXWrBggfbu3at9+/bVOku9Y8cO3XbbbXrwwQc1ceJE2Ww2paen65577lFaWhp9DgJn0tPly5drzJgxKi0tVbNmzdS8eXPl5ORo6dKlWrp0qe69997T+mEfgXemf1dPNHnyZK1YsSKAFQYelywGuUWLFun666/X4sWL9c0332jJkiX6+OOP1alTJ7ndbj3xxBMqLy83u0ycg3//+9+KiYkxuwz4ydNPP6233npLr7/+OmHMAubPn69PPvlEjz32mBHGJCkhIUFPP/20cnNzNXv2bBMrRE0+/fRTffLJJxo9erTmz59fpX8n8nq9Gjt2rPr06aORI0fKZrNJkrp166bx48crNzdXzzzzTF2VjhqcSU8XL16stm3b6r///a+WL1+ur776SosXL9bVV18tSZo+fbo2bNhQV6WjFmfS1xOtXbtW27dvD2B1dYNAFuSKior07LPPVrlUonv37nr55Zdlt9t16NAhrV692sQKcS4yMzP13Xff6d577zW7FPjBRx99pFmzZumBBx7QoEGDzC4HfpCWliZJateu3Un7evbsKUk6ePBgndaE03PLLbfozTffPK2/i19++aUyMjI0bNiwk/YNHTpU4eHh+vrrr5WXlxeIUnGazqSneXl5GjduXJVbO+Li4jR58mS1bt1a0rG/3zDXmfT1eBUVFZo0aZKef/75AFVWdwhkQayiokIXXXSRGjdufNK+xMRE454UFgqov5577jk9/fTTstv5q1jflZSUaNKkSWrevLnuuusus8uBn7jdbkmVlz+daPfu3ZKkwYMH12lN8L9FixZJqvx/64lCQ0PVo0cPud1ubdq0qa5Lw1my2+3V/oAfFhamK664QpJUUFBQx1XBn6ZOnaqbb77ZEvfx8lNgEAsNDa019R+9pKJDhw51VBH86YMPPlDfvn3VuXNns0uBH3z44YfKz8/Xtddeq9DQULPLgZ9ccsklkirvC5wxY4a8Xq+kynvL/vWvf+mmm24yLoFC/bVlyxZJqvEesaP39+7cubPOasK5mThxopxOZ7X7jv781L59+7osCX6UkZGhn376STfffLPZpfgFi3rUUyUlJdqxY4e6du3KSov10KFDhzRv3jy9/fbbZpcCP/n6668lSRdccIGWLVumWbNmaffu3SoqKlKnTp10++23a8iQISZXiTN12223afHixfruu+/07LPPatasWbrnnnv07bffqk+fPho9erTZJcIP9u/fL0mKioqqdn9cXJykytsIUP9t3LhRDodD119/vdml4Cz4fD5NnDhREyZMMLsUv2GGrJ6aO3euXC4XKwTVU5MmTdIjjzzCTIqFrF27VpL0xhtvKCsrSy+++KI++ugjTZw4Uenp6frd736n1NRUk6vEmQoNDdXUqVONf2u3bt2q8ePHKy0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" + ] + }, + "metadata": { + "image/png": { + "height": 274, + "width": 434 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "total = 100000\n", + "\n", + "dims = []\n", + "prop = []\n", + "for d in range(2, 15):\n", + " x = np.random.random(size=(d, total))\n", + " inside = ((x * x).sum(axis=0) < 1).sum()\n", + " dims.append(d)\n", + " prop.append(inside / total)\n", + " \n", + "plt.plot(dims, prop);" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "e4d74660-5c01-4e92-bc97-4ecaf0b2f577", + "metadata": {}, + "outputs": [], + "source": [ + "def posterior_grid(ngrid=10, α=1, β=1, heads=6, trials=9):\n", + " grid = np.linspace(0, 1, ngrid)\n", + " prior = stats.beta(α, β).pdf(grid)\n", + " likelihood = stats.binom.pmf(heads, trials, grid)\n", + " posterior = likelihood * prior\n", + " posterior /= posterior.sum()\n", + " return posterior" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1d9b92f6-d666-4014-8a7a-56452a8cbc53", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "68190559-a068-496c-adcb-c7aa8bae08d0", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/notebooks/52_Bayesian_inference_computations.ipynb b/_sources/notebooks/52_Bayesian_inference_computations.ipynb new file mode 100644 index 00000000..fae7c085 --- /dev/null +++ b/_sources/notebooks/52_Bayesian_inference_computations.ipynb @@ -0,0 +1,568 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c53eb8f5-80a7-4330-9f13-63220177fcc0", + "metadata": { + "tags": [] + }, + "source": [ + "# Section 5.2 — Bayesian inference computations\n", + "\n", + "This notebook contains the code examples from [Section 5.2 Bayesian inference computations]() from the **No Bullshit Guide to Statistics**." + ] + }, + { + "cell_type": "markdown", + "id": "a2d8dda2-58a9-424e-9fb3-32ad6e8777d8", + "metadata": { + "tags": [] + }, + "source": [ + "#### Notebook setup" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "aea0223e-aee9-4875-a714-897b6646baaa", + "metadata": {}, + "outputs": [], + "source": [ + "# load Python modules\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "efd86c5a-c9d2-4eab-b67d-a65e39b23ef2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Figures setup\n", + "plt.clf() # needed otherwise `sns.set_theme` doesn\"t work\n", + "from plot_helpers import RCPARAMS\n", + "RCPARAMS.update({\"figure.figsize\": (5, 3)}) # good for screen\n", + "# RCPARAMS.update({\"figure.figsize\": (5, 1.6)}) # good for print\n", + "sns.set_theme(\n", + " context=\"paper\",\n", + " style=\"whitegrid\",\n", + " palette=\"colorblind\",\n", + " rc=RCPARAMS,\n", + ")\n", + "\n", + "# High-resolution please\n", + "%config InlineBackend.figure_format = \"retina\"\n", + "\n", + "# Where to store figures\n", + "DESTDIR = \"figures/bayesian/computations\"" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "df811a10-417d-4389-8bff-30e59b5f6aef", + "metadata": {}, + "outputs": [], + "source": [ + "# set random seed for repeatability\n", + "np.random.seed(42)\n", + "#######################################################" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b473f755-7ed8-414e-819b-609cd9220b7d", + "metadata": {}, + "outputs": [], + "source": [ + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "1292b1c9-a986-4b91-8556-8fd1ac00da53", + "metadata": {}, + "source": [ + "## Example 1: estimating the probability of a biased coin" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "953b1bb0-ff29-49d0-a597-c3ce7dbffed0", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import bernoulli\n", + "tosses = bernoulli(0.7).rvs(20)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "bcbb2198-3b4b-4ede-9cde-2348a9cf00f3", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [p]\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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" + ], + "text/plain": [ + " mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail \\\n", + "p 0.688 0.092 0.522 0.861 0.002 0.002 1601.0 2528.0 \n", + "\n", + " r_hat \n", + "p 1.0 " + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import arviz as az\n", + "az.summary(idata)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "1745b4ca-a337-4a19-bf71-176bcc4e9165", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [p, y_obs]\n", + "Sampling: [y_obs]\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 773, + "width": 764 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(4, 1, figsize=(9, 9))\n", + "\n", + "for idx, n_d, dist in zip((1, 3), (\"Prior\", \"Posterior\"), pred_dists):\n", + " az.plot_dist(dist.sum(-1), \n", + " hist_kwargs={\"color\":\"0.5\", \"bins\":range(0, 22)},\n", + " ax=axes[idx])\n", + " axes[idx].set_title(f\"{n_d} predictive distribution\", fontweight='bold')\n", + " axes[idx].set_xlim(-1, 21)\n", + " axes[idx].set_ylim(0, 0.15)\n", + " axes[idx].set_xlabel(\"number of success\")\n", + "\n", + "az.plot_dist(pm.draw(p, 1000),\n", + " plot_kwargs={\"color\":\"0.5\"},\n", + " fill_kwargs={'alpha':1}, ax=axes[0])\n", + "axes[0].set_title(\"Prior distribution\", fontweight='bold')\n", + "axes[0].set_xlim(0, 1)\n", + "axes[0].set_ylim(0, 4)\n", + "axes[0].tick_params(axis='both', pad=7)\n", + "axes[0].set_xlabel(\"p\")\n", + "\n", + "az.plot_dist(idata.posterior[\"p\"],\n", + " plot_kwargs={\"color\":\"0.5\"},\n", + " fill_kwargs={'alpha':1},\n", + " ax=axes[2])\n", + "axes[2].set_title(\"Posterior distribution\", fontweight='bold')\n", + "axes[2].set_xlim(0, 1)\n", + "axes[2].set_ylim(0, 5)\n", + "axes[2].tick_params(axis='both', pad=7)\n", + "axes[2].set_xlabel(\"p\");\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "9bad4afd-a779-4ec2-a642-0459a750ffc5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 447, + "width": 794 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "from scipy.stats import binom\n", + "\n", + "predictions = (binom(n=1, p=idata.posterior[\"p\"].mean()).rvs((4000, len(tosses))),\n", + " pred_dists[1])\n", + "\n", + "for d, c, l in zip(predictions, (\"C0\", \"C4\"), (\"posterior mean\", \"posterior predictive\")):\n", + " ax = az.plot_dist(d.sum(-1),\n", + " label=l,\n", + " figsize=(10, 5),\n", + " hist_kwargs={\"alpha\": 0.5, \"color\":c, \"bins\":range(0, 22)})\n", + " ax.set_yticks([])\n", + " ax.set_xlabel(\"number of success\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8327a8e1-56b7-4bbf-a964-b96bcd7d8b69", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "393d7af3-3e51-458b-ad18-1dd7e2961064", + "metadata": {}, + "source": [ + "## Discussion" + ] + }, + { + "cell_type": "markdown", + "id": "32efdf18-c42c-472c-997b-d5d39c35cef6", + "metadata": {}, + "source": [ + "### MCMC diagnostic plots\n", + "\n", + "There are several Arviz plots we can use to check if the Markov Chain Monte Carlo chains were sampling from the posterior as expected, or ..." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "d523e69b-9248-4c09-a5d6-d880e14a913b", + "metadata": {}, + "outputs": [], + "source": [ + "# az.plot_trace(idata);\n", + "# az.plot_trace(idata, kind=\"rank_bars\");\n", + "# az.plot_trace(idata, kind=\"rank_vlines\");\n", + "\n", + "# plot_cap ~= partial regression plots?\n", + "# e.g. plot_cap(model_2, fitted_2, \"weight\", ax=ax);" + ] + }, + { + "cell_type": "markdown", + "id": "42e59770-6df4-4d98-bc6b-013e95ed488b", + "metadata": {}, + "source": [ + "### Choice of priors\n", + "\n", + "Different priors lead to different posteriors.\n", + "\n", + "See `Code 1.8 and Figure 1.7` in\n", + "[chp_01.ipynb](./explorations/PyBayesianBookCode/notebooks_updated/chp_01.ipynb)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "11152a46-4fb9-409c-8714-694b3e0e22a1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 311, + "width": 407 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "from scipy.stats import beta\n", + "\n", + "x = np.linspace(0, 1, 500)\n", + "params = [(0.5, 0.5), (1, 1), (3,3), (100, 25)]\n", + "\n", + "labels = [\"Jeffreys\", \"MaxEnt\", \"Weakly Informative\",\n", + " \"Informative\"]\n", + "\n", + "_, ax = plt.subplots()\n", + "for (α, β), label, c in zip(params, labels, (0, 1, 4, 2)):\n", + " pdf = beta.pdf(x, α, β)\n", + " ax.plot(x, pdf, label=f\"{label}\", c=f\"C{c}\", lw=3)\n", + " ax.set(yticks=[], xlabel=\"θ\", title=\"Priors\")\n", + " ax.legend()\n", + "# plt.savefig(\"img/chp01/prior_informativeness_spectrum.png\")" + ] + }, + { + "cell_type": "markdown", + "id": "0ad1e1f1-001a-4f1b-88a8-0be4e2bd277b", + "metadata": {}, + "source": [ + "### Bayesian workflow\n", + "\n", + "See also [chp_09.ipynb](./explorations/PyBayesianBookCode/notebooks_updated/chp_09.ipynb)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4019a510-e3ec-4823-84ea-74f43772895d", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/notebooks/53_difference_between_means.ipynb b/_sources/notebooks/53_difference_between_means.ipynb new file mode 100644 index 00000000..1b9c067b --- /dev/null +++ b/_sources/notebooks/53_difference_between_means.ipynb @@ -0,0 +1,2776 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c53eb8f5-80a7-4330-9f13-63220177fcc0", + "metadata": { + "tags": [] + }, + "source": [ + "# Section 5.3 — Bayesian difference between means\n", + "\n", + "This notebook contains the code examples from [Section 5.3 Bayesian difference between means]() from the **No Bullshit Guide to Statistics**.\n", + "\n", + "See also [t-test.ipynb](./explorations/bambi/t-test.ipynb)\n" + ] + }, + { + "cell_type": "markdown", + "id": "a2d8dda2-58a9-424e-9fb3-32ad6e8777d8", + "metadata": { + "tags": [] + }, + "source": [ + "#### Notebook setup" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "aea0223e-aee9-4875-a714-897b6646baaa", + "metadata": {}, + "outputs": [], + "source": [ + "# load Python modules\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "efd86c5a-c9d2-4eab-b67d-a65e39b23ef2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Figures setup\n", + "plt.clf() # needed otherwise `sns.set_theme` doesn\"t work\n", + "from plot_helpers import RCPARAMS\n", + "RCPARAMS.update({\"figure.figsize\": (5, 3)}) # good for screen\n", + "# RCPARAMS.update({\"figure.figsize\": (5, 1.6)}) # good for print\n", + "sns.set_theme(\n", + " context=\"paper\",\n", + " style=\"whitegrid\",\n", + " palette=\"colorblind\",\n", + " rc=RCPARAMS,\n", + ")\n", + "\n", + "# High-resolution please\n", + "%config InlineBackend.figure_format = \"retina\"\n", + "\n", + "# Where to store figures\n", + "DESTDIR = \"figures/bayesian/dmeans\"" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "df811a10-417d-4389-8bff-30e59b5f6aef", + "metadata": {}, + "outputs": [], + "source": [ + "# set random seed for repeatability\n", + "np.random.seed(42)\n", + "#######################################################" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b473f755-7ed8-414e-819b-609cd9220b7d", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "7bdad75b-efdc-4a90-836a-62ce38d88dd2", + "metadata": {}, + "source": [ + "## Example movies genres\n", + "\n", + "see https://www.andrewheiss.com/blog/2019/01/29/diff-means-half-dozen-ways/\n", + "\n", + "see also https://bookdown.org/content/3686/metric-predicted-variable-on-one-or-two-groups.html#two-groups\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "be3f6790-973b-4358-b21b-37538043d2f0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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titleyearratinggenregenre_numeric
0Blowing Wild19535.6Action1
1No Way Back19955.2Action1
2New Jack City19916.1Action1
3Noigwon19834.2Action1
4Tarzan and the Jungle Boy19685.2Action1
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" + ], + "text/plain": [ + " title year rating genre genre_numeric\n", + "0 Blowing Wild 1953 5.6 Action 1\n", + "1 No Way Back 1995 5.2 Action 1\n", + "2 New Jack City 1991 6.1 Action 1\n", + "3 Noigwon 1983 4.2 Action 1\n", + "4 Tarzan and the Jungle Boy 1968 5.2 Action 1" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "movies = pd.read_csv(\"../datasets/movies.csv\")\n", + "movies.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "a2d29469-678f-49a3-8347-43b06a7d968c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "genre\n", + "Action 5.2845\n", + "Comedy 5.9670\n", + "Name: rating, dtype: float64" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "movies.groupby(\"genre\")[\"rating\"].mean()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "ccfc85e6-235a-41bb-b53e-1961225d2832", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "TtestResult(statistic=-4.47525173500199, pvalue=9.976981171112132e-06, df=398.0)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from scipy.stats import ttest_ind\n", + "\n", + "actions = movies[movies[\"genre\"]==\"Action\"][\"rating\"]\n", + "comedies = movies[movies[\"genre\"]==\"Comedy\"][\"rating\"]\n", + "\n", + "ttest_ind(actions, comedies, equal_var=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "dc9e120d-2f46-42ff-bc1e-8cef602d29ea", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "TtestResult(statistic=-4.47525173500199, pvalue=9.978285839671782e-06, df=397.7995256063933)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ttest_ind(actions, comedies, equal_var=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "03d416c6-0fff-451d-a6ec-4313447db21d", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + } + ], + "source": [ + "import bambi as bmb\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d7246a95-061c-4d12-a3d0-d8e5c0d9cef6", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "97ed3700-c5c1-4d28-b324-59fdee0b406e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Formula: rating ~ 1 + C(genre, levels=levels)\n", + " Family: gaussian\n", + " Link: mu = identity\n", + " Observations: 400\n", + " Priors: \n", + " target = mu\n", + " Common-level effects\n", + " Intercept ~ Normal(mu: 0.0, sigma: 5.0)\n", + " C(genre, levels=levels) ~ Normal(mu: 0.0, sigma: 1.0)\n", + " \n", + " Auxiliary parameters\n", + " sigma ~ HalfStudentT(nu: 4.0, sigma: 1.559)\n" + ] + }, + { + "ename": "AttributeError", + "evalue": "'NoneType' object has no attribute 'model'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[44], line 16\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[38;5;66;03m# Get model description\u001b[39;00m\n\u001b[1;32m 15\u001b[0m \u001b[38;5;28mprint\u001b[39m(model_eq)\n\u001b[0;32m---> 16\u001b[0m \u001b[43mmodel_eq\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbackend\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmodel\u001b[49m\n", + "\u001b[0;31mAttributeError\u001b[0m: 'NoneType' object has no attribute 'model'" + ] + } + ], + "source": [ + "# Model formula\n", + "levels = [\"Comedy\", \"Action\"]\n", + "formula = bmb.Formula(\"rating ~ 1 + C(genre, levels=levels)\")\n", + "\n", + "# Choose custom priors \n", + "priors = {\n", + " \"Intercept\": bmb.Prior(\"Normal\", mu=0, sigma=5),\n", + " \"C(genre, levels=levels)\": bmb.Prior(\"Normal\", mu=0, sigma=1)\n", + "}\n", + "\n", + "# Build model\n", + "model_eq = bmb.Model(formula, priors=priors, data=movies)\n", + "\n", + "# Get model description\n", + "print(model_eq)" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "cc64f418-cebe-45fc-8a68-c9743a14b8cd", + "metadata": {}, + "outputs": [], + "source": [ + "# model_eq.build()\n", + "# model_eq.graph()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "6e1a3f52-7ff6-4604-ae8c-3e7632067b05", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [rating_sigma, Intercept, C(genre, levels=levels)]\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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medianmadeti_3%eti_97%mcse_medianess_medianess_tailr_hat
Intercept5.9560.0725.7596.1610.0025919.2852712.01.0
C(genre, levels=levels)[Action]-0.6630.105-0.948-0.3770.0026063.0533142.01.0
rating_sigma1.5250.0371.4311.6330.0015276.6563283.01.0
\n", + "
" + ], + "text/plain": [ + " median mad eti_3% eti_97% mcse_median \\\n", + "Intercept 5.956 0.072 5.759 6.161 0.002 \n", + "C(genre, levels=levels)[Action] -0.663 0.105 -0.948 -0.377 0.002 \n", + "rating_sigma 1.525 0.037 1.431 1.633 0.001 \n", + "\n", + " ess_median ess_tail r_hat \n", + "Intercept 5919.285 2712.0 1.0 \n", + "C(genre, levels=levels)[Action] 6063.053 3142.0 1.0 \n", + "rating_sigma 5276.656 3283.0 1.0 " + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import arviz as az\n", + "az.summary(idata_eq, stat_focus=\"median\")" + ] + }, + { + "cell_type": "markdown", + "id": "b5b76140-3133-41a5-8ef9-3c997b69b602", + "metadata": {}, + "source": [ + "### Regression, assuming unequal variances\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "ad794f56-e62e-455d-bbd0-ab0733cd6c5b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Formula: rating ~ 1 + C(genre,levels=levels)\n", + " sigma ~ C(genre,levels=levels)\n", + " Family: gaussian\n", + " Link: mu = identity\n", + " sigma = log\n", + " Observations: 400\n", + " Priors: \n", + " target = mu\n", + " Common-level effects\n", + " Intercept ~ Normal(mu: 0.0, sigma: 5.0)\n", + " C(genre, levels=levels) ~ Normal(mu: 0.0, sigma: 1.0)\n", + " target = sigma\n", + " Common-level effects\n", + " sigma_Intercept ~ Normal(mu: 0.0, sigma: 1.0)\n", + " sigma_C(genre, levels=levels) ~ Cauchy(alpha: 0.0, beta: 1.0)\n" + ] + } + ], + "source": [ + "levels = [\"Comedy\", \"Action\"]\n", + "formula_uneq = bmb.Formula(\"rating ~ 1 + C(genre,levels=levels)\", \"sigma ~ C(genre,levels=levels)\")\n", + "\n", + "priors = {\n", + " \"Intercept\": bmb.Prior(\"Normal\", mu=0, sigma=5),\n", + " \"C(genre, levels=levels)\": bmb.Prior(\"Normal\", mu=0, sigma=1),\n", + " \"sigma\": {\"C(genre, levels=levels)\": bmb.Prior(\"Cauchy\", alpha=0, beta=1)},\n", + "}\n", + "\n", + "# Build model\n", + "model_uneq = bmb.Model(formula_uneq, priors=priors, data=movies)\n", + "\n", + "# Get model description\n", + "print(model_uneq)\n", + "# model_uneq.build()\n", + "# model_uneq.graph()" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "ce4c0ce1-10d1-41c3-84da-0d8e0d04e19f", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [Intercept, C(genre, levels=levels), sigma_Intercept, sigma_C(genre, levels=levels)]\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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medianmadeti_3%eti_97%mcse_medianess_medianess_tailr_hat
Intercept5.9580.0755.7536.1510.0025501.0803402.01.0
C(genre, levels=levels)[Action]-0.6670.101-0.940-0.3840.0036121.2313284.01.0
sigma_Intercept0.4340.0340.3400.5330.0016062.6343350.01.0
sigma_C(genre, levels=levels)[Action]-0.0230.047-0.1540.1130.0015655.4603044.01.0
sigma[0]1.5070.0501.3771.6600.0016215.9972575.01.0
...........................
sigma[395]1.5440.0531.4061.7030.0016062.6343350.01.0
sigma[396]1.5440.0531.4061.7030.0016062.6343350.01.0
sigma[397]1.5440.0531.4061.7030.0016062.6343350.01.0
sigma[398]1.5440.0531.4061.7030.0016062.6343350.01.0
sigma[399]1.5440.0531.4061.7030.0016062.6343350.01.0
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" + ], + "text/plain": [ + " median mad eti_3% eti_97% \\\n", + "Intercept 5.958 0.075 5.753 6.151 \n", + "C(genre, levels=levels)[Action] -0.667 0.101 -0.940 -0.384 \n", + "sigma_Intercept 0.434 0.034 0.340 0.533 \n", + "sigma_C(genre, levels=levels)[Action] -0.023 0.047 -0.154 0.113 \n", + "sigma[0] 1.507 0.050 1.377 1.660 \n", + "... ... ... ... ... \n", + "sigma[395] 1.544 0.053 1.406 1.703 \n", + "sigma[396] 1.544 0.053 1.406 1.703 \n", + "sigma[397] 1.544 0.053 1.406 1.703 \n", + "sigma[398] 1.544 0.053 1.406 1.703 \n", + "sigma[399] 1.544 0.053 1.406 1.703 \n", + "\n", + " mcse_median ess_median ess_tail \\\n", + "Intercept 0.002 5501.080 3402.0 \n", + "C(genre, levels=levels)[Action] 0.003 6121.231 3284.0 \n", + "sigma_Intercept 0.001 6062.634 3350.0 \n", + "sigma_C(genre, levels=levels)[Action] 0.001 5655.460 3044.0 \n", + "sigma[0] 0.001 6215.997 2575.0 \n", + "... ... ... ... \n", + "sigma[395] 0.001 6062.634 3350.0 \n", + "sigma[396] 0.001 6062.634 3350.0 \n", + "sigma[397] 0.001 6062.634 3350.0 \n", + "sigma[398] 0.001 6062.634 3350.0 \n", + "sigma[399] 0.001 6062.634 3350.0 \n", + "\n", + " r_hat \n", + "Intercept 1.0 \n", + "C(genre, levels=levels)[Action] 1.0 \n", + "sigma_Intercept 1.0 \n", + "sigma_C(genre, levels=levels)[Action] 1.0 \n", + "sigma[0] 1.0 \n", + "... ... \n", + "sigma[395] 1.0 \n", + "sigma[396] 1.0 \n", + "sigma[397] 1.0 \n", + "sigma[398] 1.0 \n", + "sigma[399] 1.0 \n", + "\n", + "[404 rows x 8 columns]" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "az.summary(idata_uneq, stat_focus=\"median\")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "9b882f87-0a06-473c-9b1f-9bb3f4a98c4e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.9772624837732771" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.exp(az.summary(idata_uneq, stat_focus=\"median\").loc[\"sigma_C(genre, levels=levels)[Action]\",\"median\"])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f7e73b05-6479-472c-95f7-4b58a44864f1", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "1a0b138c-5cd3-4733-971f-0c64a146bb12", + "metadata": {}, + "source": [ + "### BEST" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "0b9d4894-d31b-4bde-870f-0f4641d8a0a6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Formula: rating ~ 1 + C(genre,levels=levels)\n", + " sigma ~ C(genre,levels=levels)\n", + " Family: t\n", + " Link: mu = identity\n", + " sigma = log\n", + " Observations: 400\n", + " Priors: \n", + " target = mu\n", + " Common-level effects\n", + " Intercept ~ Normal(mu: 0.0, sigma: 5.0)\n", + " C(genre, levels=levels) ~ Normal(mu: 0.0, sigma: 1.0)\n", + " \n", + " Auxiliary parameters\n", + " nu ~ Exponential(lam: 0.0345)\n", + " target = sigma\n", + " Common-level effects\n", + " sigma_Intercept ~ Normal(mu: 0.0, sigma: 1.0)\n", + " sigma_C(genre, levels=levels) ~ Cauchy(alpha: 0.0, beta: 1.0)\n" + ] + } + ], + "source": [ + "levels = [\"Comedy\", \"Action\"]\n", + "formula_best = bmb.Formula(\"rating ~ 1 + C(genre,levels=levels)\", \"sigma ~ C(genre,levels=levels)\")\n", + "\n", + "priors = {\n", + " \"Intercept\": bmb.Prior(\"Normal\", mu=0, sigma=5),\n", + " \"C(genre, levels=levels)\": bmb.Prior(\"Normal\", mu=0, sigma=1),\n", + " \"sigma\": {\"C(genre, levels=levels)\": bmb.Prior(\"Cauchy\", alpha=0, beta=1)},\n", + " \"nu\": bmb.Prior(\"Exponential\", lam=1/29),\n", + "}\n", + "\n", + "# Build model\n", + "model_best = bmb.Model(formula_best, priors=priors, family=\"t\", data=movies)\n", + "\n", + "# Get model description\n", + "print(model_best)\n", + "# model_best.build()\n", + "# model_best.graph()" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "d953cca3-3f52-4af0-b6ff-d660b36b7752", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [rating_nu, Intercept, C(genre, levels=levels), sigma_Intercept, sigma_C(genre, levels=levels)]\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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medianmadeti_3%eti_97%mcse_medianess_medianess_tailr_hat
Intercept5.9810.0705.7876.1720.0024154.8202915.01.0
C(genre, levels=levels)[Action]-0.6800.100-0.960-0.4020.0033883.9132685.01.0
sigma_Intercept0.3870.0400.2680.4950.0023197.4442080.01.0
sigma_C(genre, levels=levels)[Action]0.0000.051-0.1420.1440.0023651.1212894.01.0
rating_nu32.07913.9559.874105.4160.4553032.6442062.01.0
...........................
sigma[395]1.4720.0591.3071.6400.0023197.4442080.01.0
sigma[396]1.4720.0591.3071.6400.0023197.4442080.01.0
sigma[397]1.4720.0591.3071.6400.0023197.4442080.01.0
sigma[398]1.4720.0591.3071.6400.0023197.4442080.01.0
sigma[399]1.4720.0591.3071.6400.0023197.4442080.01.0
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405 rows × 8 columns

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" + ], + "text/plain": [ + " median mad eti_3% eti_97% \\\n", + "Intercept 5.981 0.070 5.787 6.172 \n", + "C(genre, levels=levels)[Action] -0.680 0.100 -0.960 -0.402 \n", + "sigma_Intercept 0.387 0.040 0.268 0.495 \n", + "sigma_C(genre, levels=levels)[Action] 0.000 0.051 -0.142 0.144 \n", + "rating_nu 32.079 13.955 9.874 105.416 \n", + "... ... ... ... ... \n", + "sigma[395] 1.472 0.059 1.307 1.640 \n", + "sigma[396] 1.472 0.059 1.307 1.640 \n", + "sigma[397] 1.472 0.059 1.307 1.640 \n", + "sigma[398] 1.472 0.059 1.307 1.640 \n", + "sigma[399] 1.472 0.059 1.307 1.640 \n", + "\n", + " mcse_median ess_median ess_tail \\\n", + "Intercept 0.002 4154.820 2915.0 \n", + "C(genre, levels=levels)[Action] 0.003 3883.913 2685.0 \n", + "sigma_Intercept 0.002 3197.444 2080.0 \n", + "sigma_C(genre, levels=levels)[Action] 0.002 3651.121 2894.0 \n", + "rating_nu 0.455 3032.644 2062.0 \n", + "... ... ... ... \n", + "sigma[395] 0.002 3197.444 2080.0 \n", + "sigma[396] 0.002 3197.444 2080.0 \n", + "sigma[397] 0.002 3197.444 2080.0 \n", + "sigma[398] 0.002 3197.444 2080.0 \n", + "sigma[399] 0.002 3197.444 2080.0 \n", + "\n", + " r_hat \n", + "Intercept 1.0 \n", + "C(genre, levels=levels)[Action] 1.0 \n", + "sigma_Intercept 1.0 \n", + "sigma_C(genre, levels=levels)[Action] 1.0 \n", + "rating_nu 1.0 \n", + "... ... \n", + "sigma[395] 1.0 \n", + "sigma[396] 1.0 \n", + "sigma[397] 1.0 \n", + "sigma[398] 1.0 \n", + "sigma[399] 1.0 \n", + "\n", + "[405 rows x 8 columns]" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "az.summary(idata_best, stat_focus=\"median\")" + ] + }, + { + "cell_type": "markdown", + "id": "10f4dbfe-ce60-4055-8224-fc0621c8a1e6", + "metadata": {}, + "source": [ + "### BEST with priors on variables instead of difference\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "6e76947c-5f64-45af-9526-7d6c78456845", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Formula: rating ~ 0 + C(genre,levels=levels)\n", + " sigma ~ 0 + C(genre,levels=levels)\n", + " Family: t\n", + " Link: mu = identity\n", + " sigma = log\n", + " Observations: 400\n", + " Priors: \n", + " target = mu\n", + " Common-level effects\n", + " C(genre, levels=levels) ~ TruncatedNormal(mu: 6.0, sigma: 2.0, lower: 1.0, upper: 10.0)\n", + " \n", + " Auxiliary parameters\n", + " nu ~ Exponential(lam: 0.0345)\n", + " target = sigma\n", + " Common-level effects\n", + " sigma_C(genre, levels=levels) ~ Cauchy(alpha: 0.0, beta: 1.0)\n" + ] + } + ], + "source": [ + "levels = [\"Comedy\", \"Action\"]\n", + "formula_best2 = bmb.Formula(\"rating ~ 0 + C(genre,levels=levels)\",\n", + " \"sigma ~ 0 + C(genre,levels=levels)\")\n", + "\n", + "priors = {\n", + " \"C(genre, levels=levels)\": bmb.Prior(\"TruncatedNormal\", mu=6, sigma=2, lower=1, upper=10),\n", + " \"sigma\": {\"C(genre, levels=levels)\": bmb.Prior(\"Cauchy\", alpha=0, beta=1)},\n", + " \"nu\": bmb.Prior(\"Exponential\", lam=1/29),\n", + "}\n", + "\n", + "# Build model\n", + "model_best2 = bmb.Model(formula_best2, priors=priors, family=\"t\", data=movies)\n", + "\n", + "# Get model description\n", + "print(model_best2)\n", + "# model_best2.build()\n", + "# model_best2.graph()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "7f04782d-6a8b-4c25-8f75-0091a92b8af7", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [rating_nu, C(genre, levels=levels), sigma_C(genre, levels=levels)]\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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\n", + " " + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 22 seconds.\n", + "There were 7 divergences after tuning. Increase `target_accept` or reparameterize.\n" + ] + } + ], + "source": [ + "idata_best2 = model_best2.fit(draws=1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "ef71e76d-2176-4b6f-a467-d87c49039806", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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medianmadeti_3%eti_97%mcse_medianess_medianess_tailr_hat
sigma_C(genre, levels=levels)[Comedy]0.3850.0400.2620.4970.0013433.9092076.01.0
sigma_C(genre, levels=levels)[Action]0.3840.0370.2800.4890.0013515.3782336.01.0
rating_nu30.34513.4209.972105.7260.4202940.6612236.01.0
C(genre, levels=levels)[Comedy]5.9900.0705.7766.1900.0023812.9292820.01.0
C(genre, levels=levels)[Action]5.2940.0745.0905.4930.0023737.3402513.01.0
...........................
sigma[395]1.4690.0591.3001.6440.0023433.9092076.01.0
sigma[396]1.4690.0591.3001.6440.0023433.9092076.01.0
sigma[397]1.4690.0591.3001.6440.0023433.9092076.01.0
sigma[398]1.4690.0591.3001.6440.0023433.9092076.01.0
sigma[399]1.4690.0591.3001.6440.0023433.9092076.01.0
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405 rows × 8 columns

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" + ], + "text/plain": [ + " median mad eti_3% eti_97% \\\n", + "sigma_C(genre, levels=levels)[Comedy] 0.385 0.040 0.262 0.497 \n", + "sigma_C(genre, levels=levels)[Action] 0.384 0.037 0.280 0.489 \n", + "rating_nu 30.345 13.420 9.972 105.726 \n", + "C(genre, levels=levels)[Comedy] 5.990 0.070 5.776 6.190 \n", + "C(genre, levels=levels)[Action] 5.294 0.074 5.090 5.493 \n", + "... ... ... ... ... \n", + "sigma[395] 1.469 0.059 1.300 1.644 \n", + "sigma[396] 1.469 0.059 1.300 1.644 \n", + "sigma[397] 1.469 0.059 1.300 1.644 \n", + "sigma[398] 1.469 0.059 1.300 1.644 \n", + "sigma[399] 1.469 0.059 1.300 1.644 \n", + "\n", + " mcse_median ess_median ess_tail \\\n", + "sigma_C(genre, levels=levels)[Comedy] 0.001 3433.909 2076.0 \n", + "sigma_C(genre, levels=levels)[Action] 0.001 3515.378 2336.0 \n", + "rating_nu 0.420 2940.661 2236.0 \n", + "C(genre, levels=levels)[Comedy] 0.002 3812.929 2820.0 \n", + "C(genre, levels=levels)[Action] 0.002 3737.340 2513.0 \n", + "... ... ... ... \n", + "sigma[395] 0.002 3433.909 2076.0 \n", + "sigma[396] 0.002 3433.909 2076.0 \n", + "sigma[397] 0.002 3433.909 2076.0 \n", + "sigma[398] 0.002 3433.909 2076.0 \n", + "sigma[399] 0.002 3433.909 2076.0 \n", + "\n", + " r_hat \n", + "sigma_C(genre, levels=levels)[Comedy] 1.0 \n", + "sigma_C(genre, levels=levels)[Action] 1.0 \n", + "rating_nu 1.0 \n", + "C(genre, levels=levels)[Comedy] 1.0 \n", + "C(genre, levels=levels)[Action] 1.0 \n", + "... ... \n", + "sigma[395] 1.0 \n", + "sigma[396] 1.0 \n", + "sigma[397] 1.0 \n", + "sigma[398] 1.0 \n", + "sigma[399] 1.0 \n", + "\n", + "[405 rows x 8 columns]" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "az.summary(idata_best2, stat_focus=\"median\")" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "603d0d96-f285-49e3-8d0b-44e4a2aee249", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.4681454416819895" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.exp(az.summary(idata_best2, stat_focus=\"median\").loc[\"sigma_C(genre, levels=levels)[Action]\",\"median\"])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b0a0cd8f-7ee8-4973-b3a6-12d10710ba99", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "520ee7a4-c570-4f85-8197-0f7467c00c18", + "metadata": {}, + "source": [ + "## Example from original BEST paper\n", + "\n", + "Data taken from `BESTexample-original.R` in `BEST.zip`\n", + "via https://web.archive.org/web/20170708173718/https://www.indiana.edu/~kruschke/BEST/\n", + "\n", + "\n", + "Steps following Matti Vuorre's [blog post](https://mvuorre.github.io/posts/2017-01-02-how-to-compare-two-groups-with-robust-bayesian-estimation-using-r-stan-and-brms/) see also [src](https://github.com/mvuorre/mvuorre.github.io/tree/main/posts/2017-01-02-how-to-compare-two-groups-with-robust-bayesian-estimation-using-r-stan-and-brms) notebook." + ] + }, + { + "cell_type": "markdown", + "id": "4fbc66ea-6f70-45f1-ac1b-1643a2d97744", + "metadata": {}, + "source": [ + "### Data" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "c4bba0e0-c5ab-4421-8030-cc018aec7ca2", + "metadata": {}, + "outputs": [], + "source": [ + "treated = np.array([101, 100, 102, 104, 102, 97, 105, 105, 98, 101, 100, 123, 105,\n", + " 103, 100, 95, 102, 106, 109, 102, 82, 102, 100, 102, 102, 101,\n", + " 102, 102, 103, 103, 97, 97, 103, 101, 97, 104, 96, 103, 124,\n", + " 101, 101, 100, 101, 101, 104, 100, 101])\n", + "controls = np.array([ 99, 101, 100, 101, 102, 100, 97, 101, 104, 101, 102, 102, 100,\n", + " 105, 88, 101, 100, 104, 100, 100, 100, 101, 102, 103, 97, 101,\n", + " 101, 100, 101, 99, 101, 100, 100, 101, 100, 99, 101, 100, 102,\n", + " 99, 100, 99])\n", + "d = pd.DataFrame({\n", + " \"group\": [\"treatment\"]*len(treated) + [\"control\"]*len(controls), \n", + " \"iq\": np.concatenate([treated, controls])\n", + "})" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "32653699-1c20-4fc0-a535-bbcae3d43cef", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "image/png": { + "height": 293, + "width": 450 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "sns.histplot(data=d, x=\"iq\", hue=\"group\");" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "14ad253d-c7d7-4350-919a-0fc810de02c6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
iq
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" + ], + "text/plain": [ + " iq\n", + "group \n", + "control 100.357143\n", + "treatment 101.914894" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d.groupby(\"group\").mean()" + ] + }, + { + "cell_type": "markdown", + "id": "2e01bedf-4f0d-4512-b7e2-f5b3bbb2f175", + "metadata": {}, + "source": [ + "### Equal variances t-test" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "a765681a-981b-4a9c-8311-db747843235b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1.5586953301521096, 0.12269895509665575)" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from scipy.stats import ttest_ind\n", + "\n", + "res_eqvar = ttest_ind(treated, controls, equal_var=True)\n", + "res_eqvar.statistic, res_eqvar.pvalue" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "588bb63c-7154-4ec9-bd34-f2285358f012", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[-0.42865302979133335, 3.5441545495481668]" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ci_eqvar = res_eqvar.confidence_interval(confidence_level=0.95)\n", + "[ci_eqvar.low, ci_eqvar.high]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d9ca14d2-9d26-4423-ad12-72bfe99b4490", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "460c9ad9-81b6-4d90-97ae-295bd445dcea", + "metadata": {}, + "source": [ + "### Unequal variances t-test" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "a0670103-e5bf-4dea-a6d3-c4998ca63a03", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1.622190457290228, 0.10975381983712831)" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res_uneqvar = ttest_ind(treated, controls, equal_var=False)\n", + "res_uneqvar.statistic, res_uneqvar.pvalue" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "76d367ad-94a2-4353-8115-1d3e9d015d27", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[-0.3611847716497789, 3.476686291406612]" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ci_uneqvar = res_uneqvar.confidence_interval(confidence_level=0.95)\n", + "[ci_uneqvar.low, ci_uneqvar.high]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "19a7e676-a01c-4889-b861-36ba87d3e7a6", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "2e5350f9-f505-4452-a779-c9e029b6d60a", + "metadata": {}, + "source": [ + "### Linear model" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "0df340d4-887e-49ab-bf95-fb959f276884", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: iq R-squared: 0.027\n", + "Model: OLS Adj. R-squared: 0.016\n", + "Method: Least Squares F-statistic: 2.430\n", + "Date: Mon, 19 Aug 2024 Prob (F-statistic): 0.123\n", + "Time: 22:59:33 Log-Likelihood: -263.13\n", + "No. Observations: 89 AIC: 530.3\n", + "Df Residuals: 87 BIC: 535.2\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "=========================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "-----------------------------------------------------------------------------------------\n", + "Intercept 100.3571 0.726 138.184 0.000 98.914 101.801\n", + "C(group)[T.treatment] 1.5578 0.999 1.559 0.123 -0.429 3.544\n", + "==============================================================================\n", + "Omnibus: 46.068 Durbin-Watson: 2.025\n", + "Prob(Omnibus): 0.000 Jarque-Bera (JB): 553.494\n", + "Skew: 1.108 Prob(JB): 6.46e-121\n", + "Kurtosis: 15.014 Cond. No. 2.69\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" + ] + } + ], + "source": [ + "import statsmodels.formula.api as smf\n", + "res_ols = smf.ols(\"iq ~ 1 + C(group)\", data=d).fit()\n", + "print(res_ols.summary())" + ] + }, + { + "cell_type": "markdown", + "id": "96f50bd1-8d26-433b-ac3f-1b2c56feea05", + "metadata": {}, + "source": [ + "### Alternative linear model\n", + "\n", + "Using generalized least squares to reproduce the unequal variance case." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "2a75cf9c-9ba0-4b1d-a3b8-f9823a120342", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " GLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: iq R-squared: 0.029\n", + "Model: GLS Adj. R-squared: 0.018\n", + "Method: Least Squares F-statistic: 2.629\n", + "Date: Mon, 19 Aug 2024 Prob (F-statistic): 0.109\n", + "Time: 22:59:33 Log-Likelihood: -248.41\n", + "No. Observations: 89 AIC: 500.8\n", + "Df Residuals: 87 BIC: 505.8\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "=========================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "-----------------------------------------------------------------------------------------\n", + "Intercept 100.3571 0.388 258.627 0.000 99.586 101.128\n", + "C(group)[T.treatment] 1.5578 0.961 1.622 0.109 -0.352 3.467\n", + "==============================================================================\n", + "Omnibus: 33.582 Durbin-Watson: 2.234\n", + "Prob(Omnibus): 0.000 Jarque-Bera (JB): 346.198\n", + "Skew: -0.648 Prob(JB): 6.67e-76\n", + "Kurtosis: 12.575 Cond. No. 2.79\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" + ] + } + ], + "source": [ + "n_t, var_t = len(treated), treated.var()\n", + "n_c, var_c = len(controls), controls.var()\n", + "sigma2s = [var_t]*n_t + [var_c]*n_c\n", + "\n", + "res_gls = smf.gls(\"iq ~ 1 + C(group)\", data=d, sigma=sigma2s).fit()\n", + "print(res_gls.summary())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "62fc825a-650c-4176-9e9f-05c1c43e930a", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "e17037dd-55c0-4d61-b01c-8a30f6aa3501", + "metadata": {}, + "source": [ + "## Bayesian equal variances model" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "97ca996a-3ff8-4489-b193-060190419e5e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Formula: iq ~ 1 + group\n", + " Family: gaussian\n", + " Link: mu = identity\n", + " Observations: 89\n", + " Priors: \n", + " target = mu\n", + " Common-level effects\n", + " Intercept ~ Normal(mu: 101.1798, sigma: 17.17)\n", + " group ~ Normal(mu: 0.0, sigma: 23.6275)\n", + " \n", + " Auxiliary parameters\n", + " sigma ~ HalfStudentT(nu: 4.0, sigma: 4.718)\n" + ] + } + ], + "source": [ + "import bambi as bmb\n", + "\n", + "mod_eqvar = bmb.Model(\"iq ~ 1 + group\", data=d)\n", + "print(mod_eqvar)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "7a7b6ec2-d87b-4f47-a6bb-00f1e4c99ae8", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [iq_sigma, Intercept, group]\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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meansdhdi_3%hdi_97%
Intercept100.3580.72798.973101.722
group[treatment]1.5541.002-0.3583.365
iq_sigma4.7420.3604.0795.411
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" + ], + "text/plain": [ + " mean sd hdi_3% hdi_97%\n", + "Intercept 100.358 0.727 98.973 101.722\n", + "group[treatment] 1.554 1.002 -0.358 3.365\n", + "iq_sigma 4.742 0.360 4.079 5.411" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import arviz as az\n", + "\n", + "az.summary(idata_eqvar, kind=\"stats\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f05fac0c-c19f-46f4-b308-f475e0b2f2c1", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "ed3adf62-60da-4d80-81c4-638c98ecd0c5", + "metadata": {}, + "source": [ + "## Bayesian unequal variances model" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "65599934-f457-4c75-8450-f60bc7743523", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Formula: iq ~ 1 + group\n", + " sigma ~ group\n", + " Family: gaussian\n", + " Link: mu = identity\n", + " sigma = log\n", + " Observations: 89\n", + " Priors: \n", + " target = mu\n", + " Common-level effects\n", + " Intercept ~ Normal(mu: 101.1798, sigma: 17.17)\n", + " group ~ Normal(mu: 0.0, sigma: 23.6275)\n", + " target = sigma\n", + " Common-level effects\n", + " sigma_Intercept ~ Normal(mu: 0.0, sigma: 1.0)\n", + " sigma_group ~ Normal(mu: 0.0, sigma: 1.0)\n" + ] + } + ], + "source": [ + "formula = bmb.Formula(\"iq ~ 1 + group\", \"sigma ~ group\")\n", + "mod_uneqvar = bmb.Model(formula, data=d)\n", + "print(mod_uneqvar)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "c79d67df-82c2-4672-8d0a-3c83af7296cd", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [Intercept, group, sigma_Intercept, sigma_group]\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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meansdhdi_3%hdi_97%
Intercept100.3570.39799.617101.105
group[treatment]1.5530.965-0.1773.434
sigma_Intercept0.9390.1090.7411.150
sigma_group[treatment]0.8490.1510.5661.133
sigma[0]6.0130.6374.8817.212
...............
sigma[84]2.5740.2852.0683.121
sigma[85]2.5740.2852.0683.121
sigma[86]2.5740.2852.0683.121
sigma[87]2.5740.2852.0683.121
sigma[88]2.5740.2852.0683.121
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" + ], + "text/plain": [ + " mean sd hdi_3% hdi_97%\n", + "Intercept 100.357 0.397 99.617 101.105\n", + "group[treatment] 1.553 0.965 -0.177 3.434\n", + "sigma_Intercept 0.939 0.109 0.741 1.150\n", + "sigma_group[treatment] 0.849 0.151 0.566 1.133\n", + "sigma[0] 6.013 0.637 4.881 7.212\n", + "... ... ... ... ...\n", + "sigma[84] 2.574 0.285 2.068 3.121\n", + "sigma[85] 2.574 0.285 2.068 3.121\n", + "sigma[86] 2.574 0.285 2.068 3.121\n", + "sigma[87] 2.574 0.285 2.068 3.121\n", + "sigma[88] 2.574 0.285 2.068 3.121\n", + "\n", + "[93 rows x 4 columns]" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "az.summary(idata_uneqvar, kind=\"stats\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cf380df8-1049-44a8-9298-51bf3cd49258", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "a2e724c9-e853-4d9f-bd02-54473c61d022", + "metadata": {}, + "source": [ + "## Robust Bayesian Estimation" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "id": "12f66e4a-8e0f-4d2c-aa1e-b0944fbb499c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Formula: iq ~ 1 + group\n", + " sigma ~ group\n", + " Family: t\n", + " Link: mu = identity\n", + " sigma = log\n", + " Observations: 89\n", + " Priors: \n", + " target = mu\n", + " Common-level effects\n", + " Intercept ~ Normal(mu: 101.1798, sigma: 17.17)\n", + " group ~ Normal(mu: 0.0, sigma: 23.6275)\n", + " \n", + " Auxiliary parameters\n", + " nu ~ Gamma(alpha: 2.0, beta: 0.1)\n", + " target = sigma\n", + " Common-level effects\n", + " sigma_Intercept ~ Normal(mu: 0.0, sigma: 1.0)\n", + " sigma_group ~ Normal(mu: 0.0, sigma: 1.0)\n" + ] + } + ], + "source": [ + "formula = bmb.Formula(\"iq ~ 1 + group\", \"sigma ~ group\")\n", + "mod_robust = bmb.Model(formula, family=\"t\", data=d)\n", + "print(mod_robust)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "c64e2037-ba8b-4bb5-87c6-1e0bf5dffb37", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [iq_nu, Intercept, group, sigma_Intercept, sigma_group]\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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meansdhdi_3%hdi_97%
Intercept100.5250.211100.142100.931
group[treatment]1.0260.4140.2481.799
sigma_Intercept0.0090.196-0.3640.361
sigma_group[treatment]0.6240.2520.1561.090
iq_nu1.8270.4871.0902.768
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sigma[84]1.0290.2040.6771.416
sigma[85]1.0290.2040.6771.416
sigma[86]1.0290.2040.6771.416
sigma[87]1.0290.2040.6771.416
sigma[88]1.0290.2040.6771.416
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" + ], + "text/plain": [ + " mean sd hdi_3% hdi_97%\n", + "Intercept 100.525 0.211 100.142 100.931\n", + "group[treatment] 1.026 0.414 0.248 1.799\n", + "sigma_Intercept 0.009 0.196 -0.364 0.361\n", + "sigma_group[treatment] 0.624 0.252 0.156 1.090\n", + "iq_nu 1.827 0.487 1.090 2.768\n", + "... ... ... ... ...\n", + "sigma[84] 1.029 0.204 0.677 1.416\n", + "sigma[85] 1.029 0.204 0.677 1.416\n", + "sigma[86] 1.029 0.204 0.677 1.416\n", + "sigma[87] 1.029 0.204 0.677 1.416\n", + "sigma[88] 1.029 0.204 0.677 1.416\n", + "\n", + "[94 rows x 4 columns]" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "idata_robust = mod_robust.fit(draws=1000)\n", + "az.summary(idata_robust, kind=\"stats\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d8f766e1-b53a-42bc-bb1f-f01825179219", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/notebooks/54_Bayesian_linear_models.ipynb b/_sources/notebooks/54_Bayesian_linear_models.ipynb new file mode 100644 index 00000000..4459a9f7 --- /dev/null +++ b/_sources/notebooks/54_Bayesian_linear_models.ipynb @@ -0,0 +1,425 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c53eb8f5-80a7-4330-9f13-63220177fcc0", + "metadata": { + "tags": [] + }, + "source": [ + "# Section 5.4 — Bayesian linear models\n", + "\n", + "This notebook contains the code examples from [Section 5.4 Bayesian linear models]() from the **No Bullshit Guide to Statistics**.\n", + "\n", + "See also examples in:\n", + "- [BambiRegression.ipynb](./explorations/BambiRegression.ipynb).\n", + "- [chp_03.ipynb](./explorations/PyBayesianBookCode/notebooks_updated/chp_03.ipynb)\n", + "- [ESCS_multiple_regression.ipynb](./explorations/bambi/ESCS_multiple_regression.ipynb)" + ] + }, + { + "cell_type": "markdown", + "id": "a2d8dda2-58a9-424e-9fb3-32ad6e8777d8", + "metadata": { + "tags": [] + }, + "source": [ + "#### Notebook setup" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "aea0223e-aee9-4875-a714-897b6646baaa", + "metadata": {}, + "outputs": [], + "source": [ + "# load Python modules\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "efd86c5a-c9d2-4eab-b67d-a65e39b23ef2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Figures setup\n", + "plt.clf() # needed otherwise `sns.set_theme` doesn\"t work\n", + "from plot_helpers import RCPARAMS\n", + "RCPARAMS.update({\"figure.figsize\": (5, 3)}) # good for screen\n", + "# RCPARAMS.update({\"figure.figsize\": (5, 1.6)}) # good for print\n", + "sns.set_theme(\n", + " context=\"paper\",\n", + " style=\"whitegrid\",\n", + " palette=\"colorblind\",\n", + " rc=RCPARAMS,\n", + ")\n", + "\n", + "# High-resolution please\n", + "%config InlineBackend.figure_format = \"retina\"\n", + "\n", + "# Where to store figures\n", + "DESTDIR = \"figures/bayesian/lms\"" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "df811a10-417d-4389-8bff-30e59b5f6aef", + "metadata": {}, + "outputs": [], + "source": [ + "# set random seed for repeatability\n", + "np.random.seed(42)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "618ce6ce-8c01-4ff1-820e-6f582e965c03", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "5b3ae1e8-7793-499a-bb27-987136fd3301", + "metadata": {}, + "source": [ + "## Simple linear regression using PyMC" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "742077e0-ca9a-4da4-af08-434e85e25575", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [beta0, beta1, sigma]\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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meansdhdi_3%hdi_97%
beta03.0060.0952.8263.183
beta11.8570.1041.6672.054
sigma0.9570.0690.8281.086
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" + ], + "text/plain": [ + " mean sd hdi_3% hdi_97%\n", + "beta0 3.006 0.095 2.826 3.183\n", + "beta1 1.857 0.104 1.667 2.054\n", + "sigma 0.957 0.069 0.828 1.086" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Posterior Summary\n", + "summary = az.summary(trace, kind=\"stats\")\n", + "summary" + ] + }, + { + "cell_type": "markdown", + "id": "9d550a2d-c54f-4b6f-ba41-e836d5db7852", + "metadata": {}, + "source": [ + "### Summary using median as focus statistic\n", + "\n", + "ETI = Equal-Tailed Interval" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "aa3dbc0b-f7af-4270-9ad3-0aee3369aa5f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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medianmadeti_3%eti_97%
beta03.0060.0652.8263.183
beta11.8560.0701.6662.053
sigma0.9530.0460.8371.096
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" + ], + "text/plain": [ + " median mad eti_3% eti_97%\n", + "beta0 3.006 0.065 2.826 3.183\n", + "beta1 1.856 0.070 1.666 2.053\n", + "sigma 0.953 0.046 0.837 1.096" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "az.summary(trace, stat_focus=\"median\", kind=\"stats\")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "278b28b7-95e5-4369-8947-c9b8e01062a2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 324, + "width": 1364 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting posterior\n", + "az.plot_posterior(trace, point_estimate=\"mean\", round_to=3);" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/notebooks/55_hierarchical_models.ipynb b/_sources/notebooks/55_hierarchical_models.ipynb new file mode 100644 index 00000000..f6418447 --- /dev/null +++ b/_sources/notebooks/55_hierarchical_models.ipynb @@ -0,0 +1,118 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c53eb8f5-80a7-4330-9f13-63220177fcc0", + "metadata": { + "tags": [] + }, + "source": [ + "# Section 5.5 — Hierarchical models\n", + "\n", + "This notebook contains the code examples from [Section 5.5 Hierarchical models]() from the **No Bullshit Guide to Statistics**." + ] + }, + { + "cell_type": "markdown", + "id": "a2d8dda2-58a9-424e-9fb3-32ad6e8777d8", + "metadata": { + "tags": [] + }, + "source": [ + "#### Notebook setup" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "aea0223e-aee9-4875-a714-897b6646baaa", + "metadata": {}, + "outputs": [], + "source": [ + "# load Python modules\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "efd86c5a-c9d2-4eab-b67d-a65e39b23ef2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Figures setup\n", + "plt.clf() # needed otherwise `sns.set_theme` doesn\"t work\n", + "from plot_helpers import RCPARAMS\n", + "RCPARAMS.update({\"figure.figsize\": (5, 3)}) # good for screen\n", + "# RCPARAMS.update({\"figure.figsize\": (5, 1.6)}) # good for print\n", + "sns.set_theme(\n", + " context=\"paper\",\n", + " style=\"whitegrid\",\n", + " palette=\"colorblind\",\n", + " rc=RCPARAMS,\n", + ")\n", + "\n", + "# High-resolution please\n", + "%config InlineBackend.figure_format = \"retina\"\n", + "\n", + "# Where to store figures\n", + "DESTDIR = \"figures/bayesian/hierarchical\"" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "df811a10-417d-4389-8bff-30e59b5f6aef", + "metadata": {}, + "outputs": [], + "source": [ + "# set random seed for repeatability\n", + "np.random.seed(42)\n", + "#######################################################" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b473f755-7ed8-414e-819b-609cd9220b7d", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/blogposts/cut_material.html b/blogposts/cut_material.html index c9b525a6..083ad9d3 100644 --- a/blogposts/cut_material.html +++ b/blogposts/cut_material.html @@ -544,6 +544,9 @@

Notebook setup +
Matplotlib is building the font cache; this may take a moment.
+
+
<Figure size 640x480 with 0 Axes>
diff --git a/datasets/movies.csv b/datasets/movies.csv new file mode 100644 index 00000000..abe6ca30 --- /dev/null +++ b/datasets/movies.csv @@ -0,0 +1,401 @@ +"title","year","rating","genre","genre_numeric" +"Blowing Wild",1953,5.6,"Action",1 +"No Way Back",1995,5.2,"Action",1 +"New Jack City",1991,6.1,"Action",1 +"Noigwon",1983,4.2,"Action",1 +"Tarzan and the Jungle Boy",1968,5.2,"Action",1 +"Operation Delta Force",1997,3.7,"Action",1 +"99 mujeres",1969,5.6,"Action",1 +"Deadly Currency",1999,4.9,"Action",1 +"Pi li huo",1995,6.1,"Action",1 +"Lamarca",1994,7.4,"Action",1 +"Quick",1993,5.2,"Action",1 +"Los Angeles Streetfighter",1985,4.2,"Action",1 +"Dune",1984,6.3,"Action",1 +"Ultimul cartus",1973,7.6,"Action",1 +"Emperor of the North Pole",1973,7,"Action",1 +"Sueurs",2002,4.4,"Action",1 +"Eagle Island",1986,5.6,"Action",1 +"Disco Godfather",1979,3.3,"Action",1 +"Comodines",1997,3.9,"Action",1 +"Deadline",1981,5.1,"Action",1 +"Fantastici tre supermen, I",1967,7.9,"Action",1 +"Escape from New York",1981,6.8,"Action",1 +"Challenge, The",1982,5.4,"Action",1 +"American Shaolin",1991,4.4,"Action",1 +"Dangerous Place, A",1995,4.5,"Action",1 +"Spie uccidono a Beirut, Le",1965,5.9,"Action",1 +"Lawnmower Man 2: Beyond Cyberspace",1996,2.4,"Action",1 +"Trionfo di Ercole, Il",1964,2.3,"Action",1 +"Strategic Air Command",1955,6.3,"Action",1 +"Angels of the City",1990,4.6,"Action",1 +"InHumanoids: The Movie",1986,5.2,"Action",1 +"Diplomatic Siege",1999,3.5,"Action",1 +"Eskapo: The Serge Osmena-Geny Lopez Story",1995,6.6,"Action",1 +"Knock Off",1998,3.8,"Action",1 +"Code Name: Wild Geese",1984,4.2,"Action",1 +"Search and Destroy",1979,4,"Action",1 +"Crime Zone",1988,4.1,"Action",1 +"Diamond Run",1996,2.6,"Action",1 +"Year of the Gun",1991,5.3,"Action",1 +"Sore Losers, The",1997,4.7,"Action",1 +"Lowball",1997,4.6,"Action",1 +"Operation Delta Force 3: Clear Target",1998,3.4,"Action",1 +"Explozia",1973,4.4,"Action",1 +"Nighthawks",1981,6.2,"Action",1 +"Final Impact",1992,3.9,"Action",1 +"Killing Cars",1986,4.4,"Action",1 +"Plato's Run",1997,4.2,"Action",1 +"Jue qiao zhi duo xing",1990,5.3,"Action",1 +"Deathsport",1978,3.7,"Action",1 +"Secret of the Ice Cave, The",1989,2.3,"Action",1 +"Barb Wire",1996,3.2,"Action",1 +"Executive Decision",1996,6.3,"Action",1 +"Red Barry",1938,5.2,"Action",1 +"Kimui jeonjaeng",1992,6.9,"Action",1 +"Castlerock",2000,4.1,"Action",1 +"Killing Machine, The",1994,4,"Action",1 +"Karate Kid, Part III, The",1989,3.9,"Action",1 +"San tau chi saidoi",2000,6.3,"Action",1 +"City Limits",1985,2.8,"Action",1 +"Sun Never Sets, The",1939,6.5,"Action",1 +"Tag: The Assassination Game",1982,5.7,"Action",1 +"Anaconda",1997,4.1,"Action",1 +"Fah",1998,5.1,"Action",1 +"Above the Law",1988,5.2,"Action",1 +"Deadly Vengeance",1981,3.2,"Action",1 +"Racket Girls",1951,2.3,"Action",1 +"Eunhaengnamoo chimdae",1996,5.6,"Action",1 +"King of the Jungle",1933,5.8,"Action",1 +"Arabian Nights",1942,6.4,"Action",1 +"Man Called Dagger, A",1967,3.8,"Action",1 +"Border Patrol",1943,6.1,"Action",1 +"Texas Lightning",1981,3.4,"Action",1 +"Abyss, The",1989,7.4,"Action",1 +"Shark Hunter",2001,3.1,"Action",1 +"Beyond Mombasa",1956,5.2,"Action",1 +"Kung Fu: Monkey, Horse, Tiger",1980,9,"Action",1 +"Gojira",1984,4.8,"Action",1 +"Balance of Power",1996,4.3,"Action",1 +"False Colors",1943,6.3,"Action",1 +"Patriot Games",1992,6.8,"Action",1 +"Trick Baby",1973,6.8,"Action",1 +"Io monaca... per tre carogne e sette peccatrici",1972,3.5,"Action",1 +"Caged Fear",1992,4.3,"Action",1 +"Little Death, The",1995,5.2,"Action",1 +"Cop on a Mission",2001,7.3,"Action",1 +"They Live",1988,6.5,"Action",1 +"Gone in 60 Seconds",1974,6.1,"Action",1 +"Evenfall",2005,8.4,"Action",1 +"Chain Lightning",1950,5.4,"Action",1 +"Teufelscamp der verlorenen Frauen",1977,4.2,"Action",1 +"Cheonnyeon ho",2003,5.8,"Action",1 +"Thin Red Line, The",1998,7.2,"Action",1 +"Brown on Resolution",1935,7.4,"Action",1 +"Bridge at Remagen, The",1969,6.5,"Action",1 +"Blade",1998,6.8,"Action",1 +"King of New York",1990,6.7,"Action",1 +"En medio de la nada",1994,5.4,"Action",1 +"Air Strike",1955,6,"Action",1 +"Escape to Athena",1979,5.2,"Action",1 +"Robin Hood",1998,5.8,"Action",1 +"Alluri Seetharama Raju",1972,6.3,"Action",1 +"Mad Max",1979,6.8,"Action",1 +"Donor, The",1997,4.6,"Action",1 +"Crazies, The",1973,5.7,"Action",1 +"Brooklyn Sonnet",2000,5.9,"Action",1 +"Fatal Conflict",2000,2.3,"Action",1 +"You Only Live Twice",1967,6.8,"Action",1 +"Breakheart Pass",1975,6.2,"Action",1 +"Hitcher, The",1986,6.8,"Action",1 +"America 3000",1986,3.7,"Action",1 +"R.I.C.C.O.",2002,5.6,"Action",1 +"Black Out",1996,4.5,"Action",1 +"Under Siege",1992,6.1,"Action",1 +"Boksuneun naui geot",2002,7.6,"Action",1 +"Da mo mi zong",1976,6.7,"Action",1 +"Thursday",1998,6.6,"Action",1 +"Ultima partita, L'",1990,3.6,"Action",1 +"Dolemite",1975,5.4,"Action",1 +"Border, The",1979,5.5,"Action",1 +"Shi jie da shai",1989,4.9,"Action",1 +"Road House",1989,5.4,"Action",1 +"Tie ma liu",1977,6.5,"Action",1 +"Wild Bunch, The",1969,8.2,"Action",1 +"Tuff Turf",1985,5,"Action",1 +"Jian hua yan yu jiang nan",1977,4.7,"Action",1 +"Double Bang",2001,5.2,"Action",1 +"Deep Freeze",2003,2.1,"Action",1 +"Yojimbo",1961,8.4,"Action",1 +"Jungle Book",1942,6.7,"Action",1 +"Expendables, The",1988,4.3,"Action",1 +"Valence Theory",2004,5.3,"Action",1 +"Night Train to Mundo Fine",1966,1.8,"Action",1 +"Bounty Hunters",1997,4.9,"Action",1 +"Hei tai yang 731 xu ji zhi sha ren gong chang",1992,4.1,"Action",1 +"Thunder",1983,3.9,"Action",1 +"In Your Face",2002,7.4,"Action",1 +"Yaroslav Mudry",1981,6.3,"Action",1 +"Miami Golem",1985,3,"Action",1 +"New York Harbor Police Boat Patrol Capturing Pirates",1903,3.9,"Action",1 +"Superman II",1980,6.5,"Action",1 +"Kala Patthar",1979,6.9,"Action",1 +"Walking Tall",2004,5.9,"Action",1 +"Fair Game",1986,5,"Action",1 +"Island of the Lost",1967,5.6,"Action",1 +"Fortunes of War",1993,5.2,"Action",1 +"Natural Born Killers",1994,6.6,"Action",1 +"Resident Evil",2002,6.2,"Action",1 +"Lost Idol, The",1990,3.4,"Action",1 +"Virtuosity",1995,5.3,"Action",1 +"Man from Hong Kong, The",1975,4.8,"Action",1 +"Hire: Hostage, The",2002,7.2,"Action",1 +"Darby's Rangers",1958,6.1,"Action",1 +"BattleQueen 2020",2001,2.9,"Action",1 +"State Property",2002,2.7,"Action",1 +"Day After Tomorrow, The",2004,6.3,"Action",1 +"Wanderers, The",1979,6.9,"Action",1 +"Midnight Confessions",1995,3.8,"Action",1 +"Where Eagles Dare",1968,7.6,"Action",1 +"Gang of Roses",2003,2.6,"Action",1 +"Lit feng chin che 2 gik chuk chuen suet",1999,5.4,"Action",1 +"Hell's Outpost",1954,6.9,"Action",1 +"Maine Dil Tujhko Diya",2002,6.8,"Action",1 +"Hermann der Cherusker - Die Schlacht im Teutoburger Wald",1967,4.4,"Action",1 +"Dance of Shiva, The",1998,6.3,"Action",1 +"Beau Geste",1966,5.6,"Action",1 +"Newton Boys, The",1998,5.7,"Action",1 +"Hellboy",2004,6.7,"Action",1 +"Balls Deep",2004,8.5,"Action",1 +"Shao Lin zi di",1974,5,"Action",1 +"F/X",1986,6.5,"Action",1 +"RoboCop 3",1993,3.2,"Action",1 +"Manhunt of Mystery Island",1945,7.1,"Action",1 +"Pratibandh",1990,6.7,"Action",1 +"Heavy Metal 2000",2000,5.1,"Action",1 +"Fire Down Below",1997,4.3,"Action",1 +"Rock, The",1996,7,"Action",1 +"Hathyar",1989,8,"Action",1 +"Ljuba",1996,3,"Action",1 +"Bloodfist IV: Die Trying",1992,3.6,"Action",1 +"Electric Dragon 80.000 V",2001,6.9,"Action",1 +"Instinct to Kill",2001,4.4,"Action",1 +"Fire Over Afghanistan",2003,4.5,"Action",1 +"Menace, La",1977,6.6,"Action",1 +"Bao li xing jing",2000,4.6,"Action",1 +"Truck Stop Women",1974,4.7,"Action",1 +"Aftershock",1990,3.5,"Action",1 +"Spartacus",1960,8,"Action",1 +"Nankyoku monogatari",1983,6.9,"Action",1 +"Enemy at the Gates",2001,7.3,"Action",1 +"Reap the Wild Wind",1942,6.4,"Action",1 +"Never Say Never Again",1983,6.1,"Action",1 +"Vital Parts",2001,3.4,"Action",1 +"Boudica",2003,5.7,"Action",1 +"Superman in Exile",1954,5.9,"Action",1 +"She",1985,3.1,"Action",1 +"Silencer, The",1999,4.3,"Action",1 +"Snow Treasure",1968,5.7,"Action",1 +"Ragazzo dal kimono d'oro, Il",1987,3.4,"Action",1 +"Vecchio testamento, Il",1962,1.6,"Action",1 +"Net Worth",2000,5.1,"Action",1 +"Osobennosti natsionalnoy okhoty",1995,7.8,"Comedy",2 +"Love with the Proper Stranger",1963,7.1,"Comedy",2 +"Front Page, The",1974,7,"Comedy",2 +"Sallah Shabati",1964,6.4,"Comedy",2 +"Love Nest",1951,5.9,"Comedy",2 +"Radio Free Steve",2000,6.2,"Comedy",2 +"Forever Female",1953,6.5,"Comedy",2 +"Honey Pot, The",1967,7.2,"Comedy",2 +"Dalu",1934,9.4,"Comedy",2 +"XXL",1997,3.8,"Comedy",2 +"Men O'War",1929,7.5,"Comedy",2 +"Fantasm Comes Again",1977,3.4,"Comedy",2 +"Consuming Passions",1988,5.1,"Comedy",2 +"Rookie Bear, The",1941,6.7,"Comedy",2 +"Menq enq, mer sarere",1970,9.6,"Comedy",2 +"Up Front",1951,7.5,"Comedy",2 +"Now You See Him, Now You Don't",1972,5.4,"Comedy",2 +"Plight of Clownana, The",2004,9.9,"Comedy",2 +"Kiss and Run",2002,7,"Comedy",2 +"Strike It Rich",1990,4.4,"Comedy",2 +"I Live My Life",1935,5.6,"Comedy",2 +"Almost an Angel",1990,4.9,"Comedy",2 +"Egged On",1926,8.8,"Comedy",2 +"Gidget",1959,6,"Comedy",2 +"Butcher Boy, The",1917,6.8,"Comedy",2 +"Leader of the Band",1987,5.2,"Comedy",2 +"Shrink Is In, The",2001,4.9,"Comedy",2 +"Girl Missing",1933,6.1,"Comedy",2 +"Life of the Party, The",1930,4.2,"Comedy",2 +"Larceny, Inc.",1942,7.4,"Comedy",2 +"Sheila Levine Is Dead and Living in New York",1975,4.6,"Comedy",2 +"Men Named Milo, Women Named Greta",2000,5.6,"Comedy",2 +"Blue Rhythm",1931,6.3,"Comedy",2 +"Sing Your Worries Away",1942,6.5,"Comedy",2 +"Zurek",2003,6.7,"Comedy",2 +"Deal of a Lifetime",1999,4.2,"Comedy",2 +"Riding High",1950,5.4,"Comedy",2 +"For Singles Only",1968,1.1,"Comedy",2 +"Laberinto de pasiones",1982,6.7,"Comedy",2 +"Yellow Cab Man, The",1950,6.6,"Comedy",2 +"I Never",2003,3.4,"Comedy",2 +"Drafty, Isn't It?",1957,6.4,"Comedy",2 +"Departamento de soltero",1971,7.7,"Comedy",2 +"Pesadilla para un rico",1996,4,"Comedy",2 +"Winter Storage",1949,7.5,"Comedy",2 +"Killer Klowns from Outer Space",1988,5.3,"Comedy",2 +"Sara Goes to Lunch",2004,8.9,"Comedy",2 +"Mickey's Pal Pluto",1933,7.1,"Comedy",2 +"What Price Pants?",1931,7.1,"Comedy",2 +"She's Got Everything",1937,6.1,"Comedy",2 +"Loving and Laughing",1971,5.5,"Comedy",2 +"Mouse on the Moon, The",1963,6.3,"Comedy",2 +"Enas ippotis gia ti Vasoula",1968,6.3,"Comedy",2 +"Family Honeymoon",1949,6.2,"Comedy",2 +"Back Roads",1981,5.3,"Comedy",2 +"Me la debes",2001,7,"Comedy",2 +"Emma",1932,6.5,"Comedy",2 +"14 Carrot Rabbit",1952,7.2,"Comedy",2 +"Monkeybone",2001,4.7,"Comedy",2 +"Loaf",1991,3.6,"Comedy",2 +"Stay Hungry",1976,5.5,"Comedy",2 +"Alle tiders kupp",1964,4.9,"Comedy",2 +"Mr. Flip",1909,2.9,"Comedy",2 +"Ernstfall in Havanna",2002,6.5,"Comedy",2 +"Breakfast of Aliens",1993,2.6,"Comedy",2 +"Blackboard Jumble",1957,6.9,"Comedy",2 +"Revenge of the Nerds II: Nerds in Paradise",1987,3.9,"Comedy",2 +"Admirable Crichton, The",1957,6.3,"Comedy",2 +"Arabesk",1989,8.4,"Comedy",2 +"Return of the Musketeers, The",1989,5.7,"Comedy",2 +"Great McGonagall, The",1974,5.5,"Comedy",2 +"Roller Coaster Rabbit",1990,7.7,"Comedy",2 +"Harry, un ami qui vous veut du bien",2000,7.2,"Comedy",2 +"Sherekilebi",1973,8.4,"Comedy",2 +"Alias St. Nick",1935,5.2,"Comedy",2 +"Let's Stalk Spinach",1951,4.7,"Comedy",2 +"Snake Tales",2000,7.5,"Comedy",2 +"Majority of One, A",1962,5.6,"Comedy",2 +"Ensign Pulver",1964,5.4,"Comedy",2 +"Going Overboard",1989,2.1,"Comedy",2 +"Hammersmith Is Out",1972,4.7,"Comedy",2 +"I.Q.",1994,6,"Comedy",2 +"Trottie True",1949,5.9,"Comedy",2 +"Se permettete parliamo di donne",1964,6.1,"Comedy",2 +"Rajio no jikan",1997,7.5,"Comedy",2 +"Fanalysis",2002,7.7,"Comedy",2 +"Jesus Henry Christ",2001,5.3,"Comedy",2 +"Faux contact",2000,6.4,"Comedy",2 +"Pigen og pressefotografen",1963,6.3,"Comedy",2 +"Smile, Darn Ya, Smile!",1931,4.7,"Comedy",2 +"On the Right Track",1981,4.9,"Comedy",2 +"Houhokekyo tonari no Yamada-kun",1999,8,"Comedy",2 +"Vita da cani",1950,7.9,"Comedy",2 +"Down and Out with the Dolls",2001,6,"Comedy",2 +"Mush and Milk",1933,7.8,"Comedy",2 +"Rock, Pretty Baby",1956,6.5,"Comedy",2 +"Phantom of the Paradise",1974,6.8,"Comedy",2 +"Bottle Rocket",1994,7.4,"Comedy",2 +"Nobleza baturra",1935,5.1,"Comedy",2 +"Fore Play",1975,4.6,"Comedy",2 +"Gothic Romance, A",2004,8.2,"Comedy",2 +"Wild and Wonderful",1964,4.9,"Comedy",2 +"Ma quando arrivano le ragazze?",2005,6.5,"Comedy",2 +"Irish and Proud of It",1938,1,"Comedy",2 +"Vie est un long fleuve tranquille, La",1988,6.6,"Comedy",2 +"Jackass: The Movie",2002,6.1,"Comedy",2 +"Country Bears, The",2002,3.7,"Comedy",2 +"XXL",2004,3.9,"Comedy",2 +"Maltese Bippy, The",1969,4,"Comedy",2 +"Rushin' Art",1936,5.2,"Comedy",2 +"Traje, El",2002,6.8,"Comedy",2 +"Pass the Ammo",1988,4.9,"Comedy",2 +"Honeymoon Hotel",1964,5.6,"Comedy",2 +"Honeymooners, The",2003,4.7,"Comedy",2 +"Captain Thunderpants",1999,5.5,"Comedy",2 +"Crimes of the Future",1970,4.7,"Comedy",2 +"Cousins",1989,6,"Comedy",2 +"Hoofs and Goofs",1957,4.2,"Comedy",2 +"Golpe de estadio",1998,7.3,"Comedy",2 +"Soul Man",1986,4.7,"Comedy",2 +"Crooks and Coronets",1969,5.8,"Comedy",2 +"Super Bitchin' Muscle Car",2004,9.2,"Comedy",2 +"Hiss and Make Up",1943,6.8,"Comedy",2 +"Casomai",2002,6.7,"Comedy",2 +"Girl Next Door, The",1953,6.5,"Comedy",2 +"Ha ett underbart liv",1992,4.9,"Comedy",2 +"I Was a Teenage Serial Killer",1993,4.6,"Comedy",2 +"Consulta del Dr. Natalio, La",2004,6.6,"Comedy",2 +"Onda Nova",1983,6.9,"Comedy",2 +"Trohonomos Varvara",1981,5.9,"Comedy",2 +"Queen for a Day",2000,4.9,"Comedy",2 +"Terms, The",2000,8.9,"Comedy",2 +"Vios kai politia",1987,8.4,"Comedy",2 +"Crazy House",1943,5.8,"Comedy",2 +"Kappert 1: Die Briefmarke - Das Remake",1995,1,"Comedy",2 +"Hello-Goodbye",1970,3.2,"Comedy",2 +"Hard Day's Night, A",1964,7.7,"Comedy",2 +"All New Adventures of Laurel & Hardy: For Love or Mummy, The",1999,3.1,"Comedy",2 +"Two Girls and a Sailor",1944,6.6,"Comedy",2 +"Hora da Estrela, A",1985,8.2,"Comedy",2 +"Vizontele",2001,7.8,"Comedy",2 +"Eternal Sunshine of the Spotless Mind",2004,8.6,"Comedy",2 +"Little Boy Blues",1999,6.3,"Comedy",2 +"Who Killed Cock Robin?",1935,7.6,"Comedy",2 +"Half-Fare Hare",1956,6.7,"Comedy",2 +"Forever Lulu",2000,5.5,"Comedy",2 +"Amazing Dr. Clitterhouse, The",1938,6.5,"Comedy",2 +"Otoko wa tsurai yo: Boku no ojisan",1989,6.9,"Comedy",2 +"Triplet Trouble",1952,6.6,"Comedy",2 +"Anne of Green Gables",1934,7.1,"Comedy",2 +"Cuisinier, le poulet, la femme et son mari",1996,8.4,"Comedy",2 +"Reaching for the Moon",1930,5.7,"Comedy",2 +"Buldoci a tresne",1981,4.6,"Comedy",2 +"Poet & Peasant, The",1945,5.6,"Comedy",2 +"You Can't Have Everything",1937,6.7,"Comedy",2 +"V.O.",2001,5.9,"Comedy",2 +"Monkey Trouble",1994,4.6,"Comedy",2 +"Purely Belter",2000,6.6,"Comedy",2 +"Knutsen & Ludvigsen",1974,4.4,"Comedy",2 +"Royal Blues",1997,6.4,"Comedy",2 +"13 Going On 30",2004,6.4,"Comedy",2 +"Mariages!",2004,5.8,"Comedy",2 +"Jimmy Walks Away",1997,6.1,"Comedy",2 +"Gay Bride, The",1934,6.8,"Comedy",2 +"Sono fotogenico",1980,5.4,"Comedy",2 +"While Supplies Last",2002,6,"Comedy",2 +"One Good Turn",1954,5.8,"Comedy",2 +"Dog Daze",1937,6.2,"Comedy",2 +"Sky Murder",1940,5,"Comedy",2 +"Private Benjamin",1980,6,"Comedy",2 +"When the Party's Over",1992,4.3,"Comedy",2 +"En un mundo nuevo",1972,7,"Comedy",2 +"Tarz and Jane and Boy and Cheeta",1976,7.6,"Comedy",2 +"Koko Flanel",1990,5.7,"Comedy",2 +"Fluttering Hearts",1927,6.8,"Comedy",2 +"Highway Runnery",1965,4.7,"Comedy",2 +"Road to Rio",1947,6.9,"Comedy",2 +"Black Mic Mac",1986,5.2,"Comedy",2 +"How've You Bean?",1933,6.2,"Comedy",2 +"On lautalla pienoinen kahvila",1952,6,"Comedy",2 +"Fifty Percent Grey",2001,7.3,"Comedy",2 +"Dahil may isang ikaw",1999,7,"Comedy",2 +"100 Mile Rule",2002,5.6,"Comedy",2 +"Blue in the Face",1995,6.4,"Comedy",2 +"Dear Mr. Prohack",1949,5.7,"Comedy",2 +"Born in Flames",1983,6.3,"Comedy",2 +"Patriotic Popeye",1957,4.6,"Comedy",2 +"Cover Girl",1944,7.2,"Comedy",2 +"Wild Gals of the Naked West",1962,2.7,"Comedy",2 +"Vagabond Lover, The",1929,5.5,"Comedy",2 +"Pensionat Paradiset",1937,6.2,"Comedy",2 +"Racconti romani",1955,4.1,"Comedy",2 +"Pups Is Pups",1930,7.7,"Comedy",2 +"Oh Jonathan, oh Jonathan!",1973,5.5,"Comedy",2 +"Chiens chauds, Les",1980,2.9,"Comedy",2 +"Trip - Die nackte Gitarre 0,5, Der",1996,3.1,"Comedy",2 +"Matinee",1993,6.3,"Comedy",2 +"Lovesick",1983,4.4,"Comedy",2 +"Affairs of Annabel, The",1938,5.9,"Comedy",2 +"Guita, La",1970,6.4,"Comedy",2 diff --git a/examples/ANOVA.html b/examples/ANOVA.html index c001f300..b4517983 100644 --- a/examples/ANOVA.html +++ b/examples/ANOVA.html @@ -704,10 +704,10 @@

Equivalence between ANOVA and OLS
<Axes: xlabel='group', ylabel='score'>
-../_images/51d4928fb5d591a7955d1b5f8373cf5dec6a1455213dde233136ef86d9b37ee1.png +../_images/7774bcf673a90801d096af56c75b8ade966e5d4951761b7c8fa5e97f6fef5aee.png
diff --git a/exercises/exercises_21_discrete_RVs.html b/exercises/exercises_21_discrete_RVs.html index 1e5bdae2..8965e8b0 100644 --- a/exercises/exercises_21_discrete_RVs.html +++ b/exercises/exercises_21_discrete_RVs.html @@ -1173,7 +1173,7 @@

E2.16#

-
array([42, 41, 35, 37, 39, 42, 40, 42, 47, 39])
+
array([36, 35, 42, 45, 54, 29, 34, 35, 44, 47])
diff --git a/exercises/exercises_35_two_sample_tests.html b/exercises/exercises_35_two_sample_tests.html index eb77c434..e11766df 100644 --- a/exercises/exercises_35_two_sample_tests.html +++ b/exercises/exercises_35_two_sample_tests.html @@ -591,7 +591,7 @@

E1. Permutation test for the sleep score sin the doctors -
0.05
+
0.0523
@@ -605,7 +605,7 @@

E1. Permutation test for the sleep score sin the doctors -
0.0524947505249475
+
0.0527947205279472
diff --git a/exercises/problems_1_data.html b/exercises/problems_1_data.html index c9d8d094..c30ffbcb 100644 --- a/exercises/problems_1_data.html +++ b/exercises/problems_1_data.html @@ -578,7 +578,7 @@

Problem {prob:bar-chart_score-vs-curriculum}
<Axes: xlabel='curriculum', ylabel='score'>

-../_images/649b4326f67ce9cd1bad270b86a168b435beeaa49407757bfa9b59f49551203c.png +../_images/926593044408511881c40a380b122f40852e750b662642f9ce787433f71e3fee.png

diff --git a/exercises/solutions/exercises_31_estimtors.html b/exercises/solutions/exercises_31_estimtors.html index f7096c03..be2dc90a 100644 --- a/exercises/solutions/exercises_31_estimtors.html +++ b/exercises/solutions/exercises_31_estimtors.html @@ -751,7 +751,7 @@

Exercise 3.4
<Axes: ylabel='Count'>

-../../_images/368cd8393957ad84ef9c4e00c5e06905d7314f306a9c5e44a5e8fadf92ae183a.png +../../_images/c35dbfab062b61a772db592a5c9640512818003e1017db9f72eb9b82e484ecc8.png @@ -797,7 +797,7 @@

Exercise 3.5
<Axes: xlabel='x', ylabel='$f_{X}$'>
-../../_images/caa638a3c0703dd601255b9c6714f15b0bb7651c33a5e096f87b79a19ab1117a.png +../../_images/d9a3b5f6671ab61689cce12eff733cbe0ed37f1ac3ad727a488eb7ec01998e7b.png
@@ -820,7 +820,7 @@

Exercise 3.5
<Axes: xlabel='x', ylabel='$f_{X}$'>

-../../_images/dadfab5ad78222d36e5a0c6495b79548e8c1df1228d8ece7bd71344cca75b162.png +../../_images/e5ca810b7a619cd61276e9a555c92d21608dd6ccd46eb9dec891ed031d5dbaed.png
@@ -843,7 +843,7 @@

Exercise 3.5
<Axes: xlabel='x', ylabel='$f_{X}$'>

-../../_images/bcfb2439bc15fbc7d378ccad8f002e88312aea6081a9a5a47085a7cf5deac4da.png +../../_images/4224a65fac69276abb3c4935776681bc0f66bdb11e863e715d5e480fd9475302.png @@ -892,7 +892,7 @@

Exercise 3.6
<Axes: xlabel='x', ylabel='$f_{X}$'>
-../../_images/e63a46c024d5db7b2880aeca1cbde9ca9fac69c6095b4a1ef90cf2507306794b.png +../../_images/ab84b393ebb4e1b01a697cf1bc37ca509b8b11f82d3487d55fb4cb87099abc3f.png @@ -930,7 +930,7 @@

Exercise 3.7
<Axes: ylabel='Density'>
-../../_images/62ba2e79c0bd4b398418659edc46860ad1668e9bef41920a2052e7ecf52e6537.png +../../_images/192bba20ecdae7da9fd6a15e53a6077b9e01a9e3fdc7f48b22652b3a789eb867.png
@@ -940,7 +940,7 @@

Exercise 3.7 -
(202.53408, 3.3433251409404448)
+
(202.59024, 3.4120250533403507)
@@ -982,7 +982,7 @@

Exercise 3.8
<Axes: ylabel='Density'>

-../../_images/22c1c3084644beeccda4e7381da3acb8d10c048a664f14ceb4c50ca36583c008.png +../../_images/b666ee31a98e09ac6daa8364b7185f0a9317d9bd7e5d70b45c12df60132d4083.png

Even when we take into account of the possible variability @@ -1039,7 +1039,7 @@

Exercise 3.9 -../../_images/e904336ae6943df01a21ef586cbe3d0f84d273468f29306f87d03e9e0c75845c.png +../../_images/f5df2a5b34d3ca25ad9b4a183a3d07ad2b72350c579fdd4d58edd4549df0682c.png @@ -1114,7 +1114,7 @@

Exercise 3.11
<Axes: ylabel='Density'>
-../../_images/b28d68010962f93796c68430f56b4fd2202e9fb21861cd75c5932b76301b42cc.png +../../_images/3681a00cf3324700010f095221675e9f5da4272b07b810bce1f19ba8856f7fc1.png

The boostrap etimates we obverve are very far from the @@ -1212,7 +1212,7 @@

Exercise 3.12
<Axes: xlabel='d', ylabel='$f_{D}$'>
-../../_images/80c6c3824d8a8799edbb0f340cc28b90bf5d8925c3dbdfa78667d9ade095e1a3.png +../../_images/a1191a35129b911e90ba286cf81891e47b38d1273ed51685304e6edc11f32126.png @@ -1237,7 +1237,7 @@

Exercise 3.13
<Axes: ylabel='Density'>
-../../_images/6ae57cd57c2eb686319db6f4eb8ac72be9125de872ca88b6d230e1e655ac13e4.png +../../_images/578fac1f096b9a2cc93e2d3e9a04dbe5a2bf52af6823d63ffe5aa79f4c45d486.png
@@ -1248,7 +1248,7 @@

Exercise 3.13 -
2.2232687845895387
+
2.2284457431181997
@@ -1278,7 +1278,7 @@

Exercise 3.14
<Axes: ylabel='Density'>

-../../_images/b92e7f6ce01cf87a7552dca25fba905bea4f92617dc1c5240a30cb3fa099eb75.png +../../_images/dc3975407047c1d030324b818ec6657508ac98b72cc9712e26b4838e09323ee7.png

@@ -1289,7 +1289,7 @@

Exercise 3.14 -
2.917825353767297
+
2.906217394092687
diff --git a/notebooks/11_intro_to_data.html b/notebooks/11_intro_to_data.html index d2b0a439..a09932f8 100644 --- a/notebooks/11_intro_to_data.html +++ b/notebooks/11_intro_to_data.html @@ -540,7 +540,7 @@

Random selection -
[1, 2, 5]
+
[6, 8, 4]
diff --git a/notebooks/12_data_in_practice.html b/notebooks/12_data_in_practice.html index 16c5db9e..6bfd8707 100644 --- a/notebooks/12_data_in_practice.html +++ b/notebooks/12_data_in_practice.html @@ -2019,7 +2019,7 @@

Strip plot of the -../_images/234e333f3f94654185f3faa9f97feba09779c36fd9b08afe20ec735e609e96d4.png +../_images/3b2196e33cc62cd5355a0cc40146bc4e09ba61c5e38c2fae348ccfc7dfb13548.png

We can enhance the strip plot by mapping the ezlvl variable to the colour (hue) of the points in the plot.

@@ -2030,7 +2030,7 @@

Strip plot of the -../_images/fe6bdb18359b5bc084d572c11aa115df8a403c44e1174e56f3e69f2934b98ec7.png +../_images/ebbe265d329064a88633b098c5a55e447392feeed8646eaaee49d53bb22cbc18.png

@@ -2078,7 +2078,7 @@

Studying the effect of
-../_images/75222ba72d4da78606636f9fa330fb97975d28eace85c044d78b75e66e2c4353.png +../_images/9955cb3ab979ab8221c4f60919b7f132690d4171ea8b126888a3ca62cf27ea6c.png
@@ -2390,7 +2390,7 @@

Electricity prices -../_images/de2813702a2bcd8a6afc5394198dd38c45af724236d7fae75f7a6ef8324348c5.png +../_images/31e2731e5a95bc2c8d59967178a6a385e2b448df6be960a8095a678421c76415.png

@@ -2520,7 +2520,7 @@

Students’ scores -../_images/2e3d8beb219883bceb9c616f611e78cfe672ac46328642af2d01cff669be171d.png +../_images/c64dd0bf274b681c19946a9eb317bc7cfc915eeb7152b7cea5deae87e904f95f.png
@@ -2644,7 +2644,7 @@

Kombucha volumes -../_images/9fd5360e7d876977cb477810a80f270dbd85191d86aab65f74e3a9086e9d2bf2.png +../_images/66007abe13528ce102c2b15016aa9fbc57e9e665399407160b4a8624bac71301.png

@@ -2772,7 +2772,7 @@

Doctors’ sleep study
-../_images/86f4c65cc9db7d0c88f506afc49406bd0ade3ae93bf3875a69bc245227a9e683.png +../_images/667f3c660c0ddb4edc790c61a2e966ad0188daf5d9a1ae25dca78bc55dc5137a.png
@@ -2939,7 +2939,7 @@

Website visitors -../_images/48e6f6f246e89e886ce68a26fb833ad5cc01f9bda1ddd94513126cada2cb9700.png +../_images/75d349e59235c0448022b23e35e53bf0bde5fadc4a0829ebfccad4862d3c5208.png

The black lines represent the estimates of the uncertainty of the true conversion rates diff --git a/notebooks/13_descriptive_statistics.html b/notebooks/13_descriptive_statistics.html index 29c37085..ac1701f2 100644 --- a/notebooks/13_descriptive_statistics.html +++ b/notebooks/13_descriptive_statistics.html @@ -1612,7 +1612,7 @@

Strip plots
<Axes: xlabel='score', ylabel='curriculum'>
-../_images/45666da5d85d1eee587014c83b1b0d0fd478e1e6a12d267500b86e562746c567.png +../_images/d925d1082c879f5cb5872c8d1a7468ca6373c171970feb1e61669388eb0483e6.png

@@ -1658,7 +1658,7 @@

Histograms -
<matplotlib.legend.Legend at 0x7f662aae2790>
+
<matplotlib.legend.Legend at 0x7fc003e14820>
 

 

 ../_images/277661225b1e76c86e3729310b44e2c25cd3f272881e7c9ee6233ed631b40ffb.png
diff --git a/notebooks/21_discrete_random_vars.html b/notebooks/21_discrete_random_vars.html
index b8a3b9df..eea68f43 100644
--- a/notebooks/21_discrete_random_vars.html
+++ b/notebooks/21_discrete_random_vars.html
@@ -1592,7 +1592,7 @@ 
Plotting the probability mass function
Requirement already satisfied: pytz>=2020.1 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from pandas>=2->ministats) (2024.1)
@@ -1600,7 +1600,7 @@ 
Plotting the probability mass function
Requirement already satisfied: zipp>=3.1.0 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from importlib-resources>=3.2.0->matplotlib>=3.7->ministats) (3.19.2)
+
Requirement already satisfied: zipp>=3.1.0 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from importlib-resources>=3.2.0->matplotlib>=3.7->ministats) (3.20.0)
 Requirement already satisfied: six in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from patsy>=0.5.4->statsmodels>=0.14.1->ministats) (1.16.0)
 

 

diff --git a/notebooks/23_inventory_discrete_dists.html b/notebooks/23_inventory_discrete_dists.html
index 5f6e0f57..205accdc 100644
--- a/notebooks/23_inventory_discrete_dists.html
+++ b/notebooks/23_inventory_discrete_dists.html
@@ -616,7 +616,7 @@ 
Notebook setup
Requirement already satisfied: pytz>=2020.1 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from pandas>=2->ministats) (2024.1)
@@ -624,7 +624,7 @@ 
Notebook setup
Requirement already satisfied: zipp>=3.1.0 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from importlib-resources>=3.2.0->matplotlib>=3.7->ministats) (3.19.2)
+
Requirement already satisfied: zipp>=3.1.0 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from importlib-resources>=3.2.0->matplotlib>=3.7->ministats) (3.20.0)
 Requirement already satisfied: six in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from patsy>=0.5.4->statsmodels>=0.14.1->ministats) (1.16.0)
 

 

diff --git a/notebooks/25_continuous_random_vars.html b/notebooks/25_continuous_random_vars.html
index 80614c5a..8bf16429 100644
--- a/notebooks/25_continuous_random_vars.html
+++ b/notebooks/25_continuous_random_vars.html
@@ -634,7 +634,7 @@ 
Notebook setup
Requirement already satisfied: pytz>=2020.1 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from pandas>=2->ministats) (2024.1)
@@ -642,7 +642,7 @@ 
Notebook setup
Requirement already satisfied: zipp>=3.1.0 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from importlib-resources>=3.2.0->matplotlib>=3.7->ministats) (3.19.2)
+
Requirement already satisfied: zipp>=3.1.0 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from importlib-resources>=3.2.0->matplotlib>=3.7->ministats) (3.20.0)
 Requirement already satisfied: six in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from patsy>=0.5.4->statsmodels>=0.14.1->ministats) (1.16.0)
 

 

@@ -1465,7 +1465,7 @@ 
Example 1: Multivariable uniform
-
<matplotlib.contour.QuadContourSet at 0x7f4c251396a0>
+
<matplotlib.contour.QuadContourSet at 0x7fa4c4b6a400>
 

 

 ../_images/03ba3c479c6a555ea789d4d52961ccde1213e2f441dc877ec6fa9ce444e104bf.png
@@ -1525,7 +1525,7 @@ 
Example 2: Kombucha volume increasing with temperature
 

 

-
<matplotlib.contour.QuadContourSet at 0x7f4c39184ca0>
+
<matplotlib.contour.QuadContourSet at 0x7fa4c5aeb7f0>
 

 

 ../_images/5131e76b2e4feb9d17e3d9356e78c050de3211c601dac96566eb2ad9d1701a26.png
@@ -1579,7 +1579,7 @@ 
Example 3: Temperature-dependent variability
-
<matplotlib.contour.QuadContourSet at 0x7f4c25d6d820>
+
<matplotlib.contour.QuadContourSet at 0x7fa4c5a2ecd0>
 

 

 ../_images/c30500c25ad22d1c238e3d9dea1dec4fa04237ca6869ac42152b84a1819f8b27.png
diff --git a/notebooks/26_inventory_continuous_dists.html b/notebooks/26_inventory_continuous_dists.html
index e950ce1c..dc993134 100644
--- a/notebooks/26_inventory_continuous_dists.html
+++ b/notebooks/26_inventory_continuous_dists.html
@@ -600,7 +600,7 @@ 
Notebook setup
Requirement already satisfied: pytz>=2020.1 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from pandas>=2->ministats) (2024.1)
@@ -608,7 +608,7 @@ 
Notebook setup
Requirement already satisfied: zipp>=3.1.0 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from importlib-resources>=3.2.0->matplotlib>=3.7->ministats) (3.19.2)
+
Requirement already satisfied: zipp>=3.1.0 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from importlib-resources>=3.2.0->matplotlib>=3.7->ministats) (3.20.0)
 Requirement already satisfied: six in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from patsy>=0.5.4->statsmodels>=0.14.1->ministats) (1.16.0)
 

 

diff --git a/notebooks/40_extra_cut_material.html b/notebooks/40_extra_cut_material.html
index 3f707a79..ef02dcb1 100644
--- a/notebooks/40_extra_cut_material.html
+++ b/notebooks/40_extra_cut_material.html
@@ -725,7 +725,7 @@ 
Partial regression plots
-
/tmp/ipykernel_3010/3264559806.py:31: UserWarning: *c* argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with *x* & *y*.  Please use the *color* keyword-argument or provide a 2D array with a single row if you intend to specify the same RGB or RGBA value for all points.
+
/tmp/ipykernel_3021/3264559806.py:31: UserWarning: *c* argument looks like a single numeric RGB or RGBA sequence, which should be avoided as value-mapping will have precedence in case its length matches with *x* & *y*.  Please use the *color* keyword-argument or provide a 2D array with a single row if you intend to specify the same RGB or RGBA value for all points.
   ax.scatter(x, y, c=h[0].get_color(), **scatter_kws)
 

 

@@ -894,7 +894,7 @@ 
Sheffé bands (several different ways)
-
<matplotlib.collections.PolyCollection at 0x7ff4546ed100>
+
<matplotlib.collections.PolyCollection at 0x7f49774ec940>
 

 

 ../_images/2b84074d2f669c2eaa973234a5ec48cd2fbc96acf5b3df525fb983870572c22e.png
@@ -1027,7 +1027,7 @@ 
Sheffé bands (several different ways)
<matplotlib.legend.Legend at 0x7ff471702790>
+
<matplotlib.legend.Legend at 0x7f49936caa60>
 

 

 ../_images/13880e32eb34785d52979791fd8aa0a93fcb2d51699410c94df5c68d6e857628.png
diff --git a/notebooks/41_simple_linear_regression.html b/notebooks/41_simple_linear_regression.html
index 3d2f7f8f..03608dee 100644
--- a/notebooks/41_simple_linear_regression.html
+++ b/notebooks/41_simple_linear_regression.html
@@ -1466,10 +1466,10 @@ 
Model summary table
-
Error in callback <function _draw_all_if_interactive at 0x7f775eef1550> (for post_execute):
+
Error in callback <function _draw_all_if_interactive at 0x7f1f34bbb310> (for post_execute):
 

 

 
---------------------------------------------------------------------------
diff --git a/notebooks/44_regression_with_categorical_predictors.html b/notebooks/44_regression_with_categorical_predictors.html
index 1b7e78b7..6a84ba29 100644
--- a/notebooks/44_regression_with_categorical_predictors.html
+++ b/notebooks/44_regression_with_categorical_predictors.html
@@ -988,10 +988,10 @@ 
Example 3: improved model for the sleep scoresExercises
 
 
  • Bonus Exercises
    • 
 
    
-
    ---------------------------------------------------------------------------
-ValueError                                Traceback (most recent call last)
-Cell In[11], line 18
-     14 ax2.set_ylabel("$x$")
-     17 filename = os.path.join(DESTDIR, "logistic_and_logit_functions.pdf")
----> 18 savefigure(fig, filename, tight_layout_kwargs=dict(w_pad=3))
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/ministats/utils.py:61, in savefigure(obj, filename, tight_layout_kwargs)
-     59 # remove surrounding whitespace as much as possible
-     60 if tight_layout_kwargs:
----> 61     fig.tight_layout(**tight_layout_kwargs)
-     62 else:
-     63     fig.tight_layout()
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/figure.py:3543, in Figure.tight_layout(self, pad, h_pad, w_pad, rect)
-   3541 previous_engine = self.get_layout_engine()
-   3542 self.set_layout_engine(engine)
--> 3543 engine.execute(self)
-   3544 if previous_engine is not None and not isinstance(
-   3545     previous_engine, (TightLayoutEngine, PlaceHolderLayoutEngine)
-   3546 ):
-   3547     _api.warn_external('The figure layout has changed to tight')
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/layout_engine.py:184, in TightLayoutEngine.execute(self, fig)
-    182 renderer = fig._get_renderer()
-    183 with getattr(renderer, "_draw_disabled", nullcontext)():
---> 184     kwargs = get_tight_layout_figure(
-    185         fig, fig.axes, get_subplotspec_list(fig.axes), renderer,
-    186         pad=info['pad'], h_pad=info['h_pad'], w_pad=info['w_pad'],
-    187         rect=info['rect'])
-    188 if kwargs:
-    189     fig.subplots_adjust(**kwargs)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/_tight_layout.py:266, in get_tight_layout_figure(fig, axes_list, subplotspec_list, renderer, pad, h_pad, w_pad, rect)
-    261         return {}
-    262     span_pairs.append((
-    263         slice(ss.rowspan.start * div_row, ss.rowspan.stop * div_row),
-    264         slice(ss.colspan.start * div_col, ss.colspan.stop * div_col)))
---> 266 kwargs = _auto_adjust_subplotpars(fig, renderer,
-    267                                   shape=(max_nrows, max_ncols),
-    268                                   span_pairs=span_pairs,
-    269                                   subplot_list=subplot_list,
-    270                                   ax_bbox_list=ax_bbox_list,
-    271                                   pad=pad, h_pad=h_pad, w_pad=w_pad)
-    273 # kwargs can be none if tight_layout fails...
-    274 if rect is not None and kwargs is not None:
-    275     # if rect is given, the whole subplots area (including
-    276     # labels) will fit into the rect instead of the
-   (...)
-    280     # auto_adjust_subplotpars twice, where the second run
-    281     # with adjusted rect parameters.
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/_tight_layout.py:82, in _auto_adjust_subplotpars(fig, renderer, shape, span_pairs, subplot_list, ax_bbox_list, pad, h_pad, w_pad, rect)
-     80 for ax in subplots:
-     81     if ax.get_visible():
----> 82         bb += [martist._get_tightbbox_for_layout_only(ax, renderer)]
-     84 tight_bbox_raw = Bbox.union(bb)
-     85 tight_bbox = fig.transFigure.inverted().transform_bbox(tight_bbox_raw)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:1415, in _get_tightbbox_for_layout_only(obj, *args, **kwargs)
-   1409 """
-   1410 Matplotlib's `.Axes.get_tightbbox` and `.Axis.get_tightbbox` support a
-   1411 *for_layout_only* kwarg; this helper tries to use the kwarg but skips it
-   1412 when encountering third-party subclasses that do not support it.
-   1413 """
-   1414 try:
--> 1415     return obj.get_tightbbox(*args, **{**kwargs, "for_layout_only": True})
-   1416 except TypeError:
-   1417     return obj.get_tightbbox(*args, **kwargs)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/axes/_base.py:4410, in _AxesBase.get_tightbbox(self, renderer, call_axes_locator, bbox_extra_artists, for_layout_only)
-   4407     bbox_artists = self.get_default_bbox_extra_artists()
-   4409 for a in bbox_artists:
--> 4410     bbox = a.get_tightbbox(renderer)
-   4411     if (bbox is not None
-   4412             and 0 < bbox.width < np.inf
-   4413             and 0 < bbox.height < np.inf):
-   4414         bb.append(bbox)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/legend.py:1026, in Legend.get_tightbbox(self, renderer)
-   1024 def get_tightbbox(self, renderer=None):
-   1025     # docstring inherited
--> 1026     return self._legend_box.get_window_extent(renderer)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:400, in OffsetBox.get_window_extent(self, renderer)
-    398 if renderer is None:
-    399     renderer = self.figure._get_renderer()
---> 400 bbox = self.get_bbox(renderer)
-    401 try:  # Some subclasses redefine get_offset to take no args.
-    402     px, py = self.get_offset(bbox, renderer)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in VPacker._get_bbox_and_child_offsets(self, renderer)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in <listcomp>(.0)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in HPacker._get_bbox_and_child_offsets(self, renderer)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in <listcomp>(.0)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in VPacker._get_bbox_and_child_offsets(self, renderer)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in <listcomp>(.0)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in HPacker._get_bbox_and_child_offsets(self, renderer)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in <listcomp>(.0)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:801, in TextArea.get_bbox(self, renderer)
-    796 def get_bbox(self, renderer):
-    797     _, h_, d_ = renderer.get_text_width_height_descent(
-    798         "lp", self._text._fontproperties,
-    799         ismath="TeX" if self._text.get_usetex() else False)
---> 801     bbox, info, yd = self._text._get_layout(renderer)
-    802     w, h = bbox.size
-    804     self._baseline_transform.clear()
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:386, in Text._get_layout(self, renderer)
-    384 clean_line, ismath = self._preprocess_math(line)
-    385 if clean_line:
---> 386     w, h, d = _get_text_metrics_with_cache(
-    387         renderer, clean_line, self._fontproperties,
-    388         ismath=ismath, dpi=self.figure.dpi)
-    389 else:
-    390     w = h = d = 0
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:97, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
-     94 """Call ``renderer.get_text_width_height_descent``, caching the results."""
-     95 # Cached based on a copy of fontprop so that later in-place mutations of
-     96 # the passed-in argument do not mess up the cache.
----> 97 return _get_text_metrics_with_cache_impl(
-     98     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:105, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
-    101 @functools.lru_cache(4096)
-    102 def _get_text_metrics_with_cache_impl(
-    103         renderer_ref, text, fontprop, ismath, dpi):
-    104     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 105     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/backends/backend_agg.py:230, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
-    226     return super().get_text_width_height_descent(s, prop, ismath)
-    228 if ismath:
-    229     ox, oy, width, height, descent, font_image = \
---> 230         self.mathtext_parser.parse(s, self.dpi, prop)
-    231     return width, height, descent
-    233 font = self._prepare_font(prop)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/mathtext.py:226, in MathTextParser.parse(self, s, dpi, prop)
-    222 # lru_cache can't decorate parse() directly because prop
-    223 # is mutable; key the cache using an internal copy (see
-    224 # text._get_text_metrics_with_cache for a similar case).
-    225 prop = prop.copy() if prop is not None else None
---> 226 return self._parse_cached(s, dpi, prop)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/mathtext.py:247, in MathTextParser._parse_cached(self, s, dpi, prop)
-    244 if self._parser is None:  # Cache the parser globally.
-    245     self.__class__._parser = _mathtext.Parser()
---> 247 box = self._parser.parse(s, fontset, fontsize, dpi)
-    248 output = _mathtext.ship(box)
-    249 if self._output_type == "vector":
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/_mathtext.py:1971, in Parser.parse(self, s, fonts_object, fontsize, dpi)
-   1968     result = self._expression.parseString(s)
-   1969 except ParseBaseException as err:
-   1970     # explain becomes a plain method on pyparsing 3 (err.explain(0)).
--> 1971     raise ValueError("\n" + ParseException.explain(err, 0)) from None
-   1972 self._state_stack = None
-   1973 self._in_subscript_or_superscript = False
-
-ValueError: 
-\text{expit}(x)
-^
-ParseFatalException: Unknown symbol: \text, found '\'  (at char 0), (line:1, col:1)
-
    
-
    
-
    Error in callback <function _draw_all_if_interactive at 0x7f187b432790> (for post_execute):
-
    
-
    
-
    ---------------------------------------------------------------------------
-ValueError                                Traceback (most recent call last)
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/pyplot.py:120, in _draw_all_if_interactive()
-    118 def _draw_all_if_interactive():
-    119     if matplotlib.is_interactive():
---> 120         draw_all()
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/_pylab_helpers.py:132, in Gcf.draw_all(cls, force)
-    130 for manager in cls.get_all_fig_managers():
-    131     if force or manager.canvas.figure.stale:
---> 132         manager.canvas.draw_idle()
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/backend_bases.py:2082, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
-   2080 if not self._is_idle_drawing:
-   2081     with self._idle_draw_cntx():
--> 2082         self.draw(*args, **kwargs)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/backends/backend_agg.py:400, in FigureCanvasAgg.draw(self)
-    396 # Acquire a lock on the shared font cache.
-    397 with RendererAgg.lock, \
-    398      (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
-    399       else nullcontext()):
---> 400     self.figure.draw(self.renderer)
-    401     # A GUI class may be need to update a window using this draw, so
-    402     # don't forget to call the superclass.
-    403     super().draw()
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
-     93 @wraps(draw)
-     94 def draw_wrapper(artist, renderer, *args, **kwargs):
----> 95     result = draw(artist, renderer, *args, **kwargs)
-     96     if renderer._rasterizing:
-     97         renderer.stop_rasterizing()
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
-     69     if artist.get_agg_filter() is not None:
-     70         renderer.start_filter()
----> 72     return draw(artist, renderer)
-     73 finally:
-     74     if artist.get_agg_filter() is not None:
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/figure.py:3175, in Figure.draw(self, renderer)
-   3172         # ValueError can occur when resizing a window.
-   3174 self.patch.draw(renderer)
--> 3175 mimage._draw_list_compositing_images(
-   3176     renderer, self, artists, self.suppressComposite)
-   3178 for sfig in self.subfigs:
-   3179     sfig.draw(renderer)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/image.py:131, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
-    129 if not_composite or not has_images:
-    130     for a in artists:
---> 131         a.draw(renderer)
-    132 else:
-    133     # Composite any adjacent images together
-    134     image_group = []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
-     69     if artist.get_agg_filter() is not None:
-     70         renderer.start_filter()
----> 72     return draw(artist, renderer)
-     73 finally:
-     74     if artist.get_agg_filter() is not None:
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/axes/_base.py:3064, in _AxesBase.draw(self, renderer)
-   3061 if artists_rasterized:
-   3062     _draw_rasterized(self.figure, artists_rasterized, renderer)
--> 3064 mimage._draw_list_compositing_images(
-   3065     renderer, self, artists, self.figure.suppressComposite)
-   3067 renderer.close_group('axes')
-   3068 self.stale = False
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/image.py:131, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
-    129 if not_composite or not has_images:
-    130     for a in artists:
---> 131         a.draw(renderer)
-    132 else:
-    133     # Composite any adjacent images together
-    134     image_group = []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
-     69     if artist.get_agg_filter() is not None:
-     70         renderer.start_filter()
----> 72     return draw(artist, renderer)
-     73 finally:
-     74     if artist.get_agg_filter() is not None:
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/legend.py:726, in Legend.draw(self, renderer)
-    722     self._legend_box.set_width(self.get_bbox_to_anchor().width - pad)
-    724 # update the location and size of the legend. This needs to
-    725 # be done in any case to clip the figure right.
---> 726 bbox = self._legend_box.get_window_extent(renderer)
-    727 self.legendPatch.set_bounds(bbox.bounds)
-    728 self.legendPatch.set_mutation_scale(fontsize)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:400, in OffsetBox.get_window_extent(self, renderer)
-    398 if renderer is None:
-    399     renderer = self.figure._get_renderer()
---> 400 bbox = self.get_bbox(renderer)
-    401 try:  # Some subclasses redefine get_offset to take no args.
-    402     px, py = self.get_offset(bbox, renderer)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in VPacker._get_bbox_and_child_offsets(self, renderer)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in <listcomp>(.0)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in HPacker._get_bbox_and_child_offsets(self, renderer)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in <listcomp>(.0)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in VPacker._get_bbox_and_child_offsets(self, renderer)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in <listcomp>(.0)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in HPacker._get_bbox_and_child_offsets(self, renderer)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in <listcomp>(.0)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:801, in TextArea.get_bbox(self, renderer)
-    796 def get_bbox(self, renderer):
-    797     _, h_, d_ = renderer.get_text_width_height_descent(
-    798         "lp", self._text._fontproperties,
-    799         ismath="TeX" if self._text.get_usetex() else False)
---> 801     bbox, info, yd = self._text._get_layout(renderer)
-    802     w, h = bbox.size
-    804     self._baseline_transform.clear()
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:386, in Text._get_layout(self, renderer)
-    384 clean_line, ismath = self._preprocess_math(line)
-    385 if clean_line:
---> 386     w, h, d = _get_text_metrics_with_cache(
-    387         renderer, clean_line, self._fontproperties,
-    388         ismath=ismath, dpi=self.figure.dpi)
-    389 else:
-    390     w = h = d = 0
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:97, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
-     94 """Call ``renderer.get_text_width_height_descent``, caching the results."""
-     95 # Cached based on a copy of fontprop so that later in-place mutations of
-     96 # the passed-in argument do not mess up the cache.
----> 97 return _get_text_metrics_with_cache_impl(
-     98     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:105, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
-    101 @functools.lru_cache(4096)
-    102 def _get_text_metrics_with_cache_impl(
-    103         renderer_ref, text, fontprop, ismath, dpi):
-    104     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 105     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/backends/backend_agg.py:230, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
-    226     return super().get_text_width_height_descent(s, prop, ismath)
-    228 if ismath:
-    229     ox, oy, width, height, descent, font_image = \
---> 230         self.mathtext_parser.parse(s, self.dpi, prop)
-    231     return width, height, descent
-    233 font = self._prepare_font(prop)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/mathtext.py:226, in MathTextParser.parse(self, s, dpi, prop)
-    222 # lru_cache can't decorate parse() directly because prop
-    223 # is mutable; key the cache using an internal copy (see
-    224 # text._get_text_metrics_with_cache for a similar case).
-    225 prop = prop.copy() if prop is not None else None
---> 226 return self._parse_cached(s, dpi, prop)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/mathtext.py:247, in MathTextParser._parse_cached(self, s, dpi, prop)
-    244 if self._parser is None:  # Cache the parser globally.
-    245     self.__class__._parser = _mathtext.Parser()
---> 247 box = self._parser.parse(s, fontset, fontsize, dpi)
-    248 output = _mathtext.ship(box)
-    249 if self._output_type == "vector":
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/_mathtext.py:1971, in Parser.parse(self, s, fonts_object, fontsize, dpi)
-   1968     result = self._expression.parseString(s)
-   1969 except ParseBaseException as err:
-   1970     # explain becomes a plain method on pyparsing 3 (err.explain(0)).
--> 1971     raise ValueError("\n" + ParseException.explain(err, 0)) from None
-   1972 self._state_stack = None
-   1973 self._in_subscript_or_superscript = False
-
-ValueError: 
-\text{expit}(x)
-^
-ParseFatalException: Unknown symbol: \text, found '\'  (at char 0), (line:1, col:1)
+
    Saved figure to figures/lm/generalized/logistic_and_logit_functions.pdf
 
    
 
    
-
    ---------------------------------------------------------------------------
-ValueError                                Traceback (most recent call last)
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/IPython/core/formatters.py:340, in BaseFormatter.__call__(self, obj)
-    338     pass
-    339 else:
---> 340     return printer(obj)
-    341 # Finally look for special method names
-    342 method = get_real_method(obj, self.print_method)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:169, in retina_figure(fig, base64, **kwargs)
-    160 def retina_figure(fig, base64=False, **kwargs):
-    161     """format a figure as a pixel-doubled (retina) PNG
-    162 
-    163     If `base64` is True, return base64-encoded str instead of raw bytes
-   (...)
-    167         base64 argument
-    168     """
---> 169     pngdata = print_figure(fig, fmt="retina", base64=False, **kwargs)
-    170     # Make sure that retina_figure acts just like print_figure and returns
-    171     # None when the figure is empty.
-    172     if pngdata is None:
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:152, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
-    149     from matplotlib.backend_bases import FigureCanvasBase
-    150     FigureCanvasBase(fig)
---> 152 fig.canvas.print_figure(bytes_io, **kw)
-    153 data = bytes_io.getvalue()
-    154 if fmt == 'svg':
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/backend_bases.py:2342, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
-   2336     renderer = _get_renderer(
-   2337         self.figure,
-   2338         functools.partial(
-   2339             print_method, orientation=orientation)
-   2340     )
-   2341     with getattr(renderer, "_draw_disabled", nullcontext)():
--> 2342         self.figure.draw(renderer)
-   2344 if bbox_inches:
-   2345     if bbox_inches == "tight":
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
-     93 @wraps(draw)
-     94 def draw_wrapper(artist, renderer, *args, **kwargs):
----> 95     result = draw(artist, renderer, *args, **kwargs)
-     96     if renderer._rasterizing:
-     97         renderer.stop_rasterizing()
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
-     69     if artist.get_agg_filter() is not None:
-     70         renderer.start_filter()
----> 72     return draw(artist, renderer)
-     73 finally:
-     74     if artist.get_agg_filter() is not None:
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/figure.py:3175, in Figure.draw(self, renderer)
-   3172         # ValueError can occur when resizing a window.
-   3174 self.patch.draw(renderer)
--> 3175 mimage._draw_list_compositing_images(
-   3176     renderer, self, artists, self.suppressComposite)
-   3178 for sfig in self.subfigs:
-   3179     sfig.draw(renderer)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/image.py:131, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
-    129 if not_composite or not has_images:
-    130     for a in artists:
---> 131         a.draw(renderer)
-    132 else:
-    133     # Composite any adjacent images together
-    134     image_group = []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
-     69     if artist.get_agg_filter() is not None:
-     70         renderer.start_filter()
----> 72     return draw(artist, renderer)
-     73 finally:
-     74     if artist.get_agg_filter() is not None:
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/axes/_base.py:3064, in _AxesBase.draw(self, renderer)
-   3061 if artists_rasterized:
-   3062     _draw_rasterized(self.figure, artists_rasterized, renderer)
--> 3064 mimage._draw_list_compositing_images(
-   3065     renderer, self, artists, self.figure.suppressComposite)
-   3067 renderer.close_group('axes')
-   3068 self.stale = False
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/image.py:131, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
-    129 if not_composite or not has_images:
-    130     for a in artists:
---> 131         a.draw(renderer)
-    132 else:
-    133     # Composite any adjacent images together
-    134     image_group = []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
-     69     if artist.get_agg_filter() is not None:
-     70         renderer.start_filter()
----> 72     return draw(artist, renderer)
-     73 finally:
-     74     if artist.get_agg_filter() is not None:
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/legend.py:726, in Legend.draw(self, renderer)
-    722     self._legend_box.set_width(self.get_bbox_to_anchor().width - pad)
-    724 # update the location and size of the legend. This needs to
-    725 # be done in any case to clip the figure right.
---> 726 bbox = self._legend_box.get_window_extent(renderer)
-    727 self.legendPatch.set_bounds(bbox.bounds)
-    728 self.legendPatch.set_mutation_scale(fontsize)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:400, in OffsetBox.get_window_extent(self, renderer)
-    398 if renderer is None:
-    399     renderer = self.figure._get_renderer()
---> 400 bbox = self.get_bbox(renderer)
-    401 try:  # Some subclasses redefine get_offset to take no args.
-    402     px, py = self.get_offset(bbox, renderer)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in VPacker._get_bbox_and_child_offsets(self, renderer)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in <listcomp>(.0)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in HPacker._get_bbox_and_child_offsets(self, renderer)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in <listcomp>(.0)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in VPacker._get_bbox_and_child_offsets(self, renderer)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in <listcomp>(.0)
-    482         if isinstance(c, PackerBase) and c.mode == "expand":
-    483             c.set_width(self.width)
---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    486 (x0, x1), xoffsets = _get_aligned_offsets(
-    487     [bbox.intervalx for bbox in bboxes], self.width, self.align)
-    488 height, yoffsets = _get_packed_offsets(
-    489     [bbox.height for bbox in bboxes], self.height, sep, self.mode)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer)
-    365 def get_bbox(self, renderer):
-    366     """Return the bbox of the offsetbox, ignoring parent offsets."""
---> 367     bbox, offsets = self._get_bbox_and_child_offsets(renderer)
-    368     return bbox
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in HPacker._get_bbox_and_child_offsets(self, renderer)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in <listcomp>(.0)
-    509 pad = self.pad * dpicor
-    510 sep = self.sep * dpicor
---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()]
-    513 if not bboxes:
-    514     return Bbox.from_bounds(0, 0, 0, 0).padded(pad), []
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:801, in TextArea.get_bbox(self, renderer)
-    796 def get_bbox(self, renderer):
-    797     _, h_, d_ = renderer.get_text_width_height_descent(
-    798         "lp", self._text._fontproperties,
-    799         ismath="TeX" if self._text.get_usetex() else False)
---> 801     bbox, info, yd = self._text._get_layout(renderer)
-    802     w, h = bbox.size
-    804     self._baseline_transform.clear()
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:386, in Text._get_layout(self, renderer)
-    384 clean_line, ismath = self._preprocess_math(line)
-    385 if clean_line:
---> 386     w, h, d = _get_text_metrics_with_cache(
-    387         renderer, clean_line, self._fontproperties,
-    388         ismath=ismath, dpi=self.figure.dpi)
-    389 else:
-    390     w = h = d = 0
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:97, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
-     94 """Call ``renderer.get_text_width_height_descent``, caching the results."""
-     95 # Cached based on a copy of fontprop so that later in-place mutations of
-     96 # the passed-in argument do not mess up the cache.
----> 97 return _get_text_metrics_with_cache_impl(
-     98     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:105, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
-    101 @functools.lru_cache(4096)
-    102 def _get_text_metrics_with_cache_impl(
-    103         renderer_ref, text, fontprop, ismath, dpi):
-    104     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 105     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/backends/backend_agg.py:230, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
-    226     return super().get_text_width_height_descent(s, prop, ismath)
-    228 if ismath:
-    229     ox, oy, width, height, descent, font_image = \
---> 230         self.mathtext_parser.parse(s, self.dpi, prop)
-    231     return width, height, descent
-    233 font = self._prepare_font(prop)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/mathtext.py:226, in MathTextParser.parse(self, s, dpi, prop)
-    222 # lru_cache can't decorate parse() directly because prop
-    223 # is mutable; key the cache using an internal copy (see
-    224 # text._get_text_metrics_with_cache for a similar case).
-    225 prop = prop.copy() if prop is not None else None
---> 226 return self._parse_cached(s, dpi, prop)
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/mathtext.py:247, in MathTextParser._parse_cached(self, s, dpi, prop)
-    244 if self._parser is None:  # Cache the parser globally.
-    245     self.__class__._parser = _mathtext.Parser()
---> 247 box = self._parser.parse(s, fontset, fontsize, dpi)
-    248 output = _mathtext.ship(box)
-    249 if self._output_type == "vector":
-
-File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/_mathtext.py:1971, in Parser.parse(self, s, fonts_object, fontsize, dpi)
-   1968     result = self._expression.parseString(s)
-   1969 except ParseBaseException as err:
-   1970     # explain becomes a plain method on pyparsing 3 (err.explain(0)).
--> 1971     raise ValueError("\n" + ParseException.explain(err, 0)) from None
-   1972 self._state_stack = None
-   1973 self._in_subscript_or_superscript = False
-
-ValueError: 
-\text{expit}(x)
-^
-ParseFatalException: Unknown symbol: \text, found '\'  (at char 0), (line:1, col:1)
-
    
-
    
-
    <Figure size 600x200 with 2 Axes>
+
    Saved figure to figures/lm/generalized/logistic_and_logit_functions.png
 
    
 
    
+../_images/1dfe18d065c7cd84fa9f8c77c33fcd0a44aa19182ee4620439b51efec08f3fd4.png

    @@ -1606,7 +833,7 @@

    Logistic regression# Plot the logistic regression model xs = np.linspace(xlims[0], xlims[1], 200) ps = expit_model(xs) - sns.lineplot(x=xs, y=ps, ax=ax, label=r"$p(x) = \text{expit}(\beta_0 + \beta_1x)$", linewidth=2) + sns.lineplot(x=xs, y=ps, ax=ax, label=r"$p(x) = \mathrm{expit}(\beta_0 + \beta_1x)$", linewidth=2) # Plot Bernoulli distributions at specified x positions x_positions = [2,4,5,6,8,10] @@ -1632,7 +859,7 @@

    Logistic regression +../_images/7037635c81105b3b63caa1767e533482a4d9d79863285f5b1b3effbb51090082.png
    @@ -1754,10 +981,10 @@

    Example 1: hiring student interns -../_images/1b9740419120924fb9e3bfd519a61117ca1fbfc349dfd752b92786a539efbb19.png +../_images/177d412a04ceb10fa9c484d9973a2e95022cecb8b2182df55c77a05d85cdff8b.png

    @@ -1807,7 +1034,7 @@

    Example 1: hiring student interns +../_images/77b8dddda53b94cfbb8c1ab358072b2fbff2eb97114c00aa7b281f5ed3b0ebc3.png

    @@ -1829,10 +1056,10 @@

    Example 1: hiring student interns +../_images/d7a4ae8a998f4cb89c56d709ecf787c03178bb6afea6843720bb0a8c4435568b.png

    @@ -2177,10 +1404,10 @@

    Example 2: hard disk failures over time 
    Saved figure to figures/lm/generalized/poisson_regression_hdisks_failures_vs_age.pdf
-Saved figure to figures/lm/generalized/poisson_regression_hdisks_failures_vs_age.png
    -../_images/d39e6b60d9ac4d4790c082b3889e86bb422068c5aff44e4fcc075fc60a1a6008.png +
    Saved figure to figures/lm/generalized/poisson_regression_hdisks_failures_vs_age.png
+
    +
    +../_images/984dd7f8d91a8ed7563622bc958a47fb16fcb896b19c2135f4653157d253f488.png
    @@ -2239,10 +1468,10 @@

    Example 2: hard disk failures over time +
    ---------------------------------------------------------------------------
+ModuleNotFoundError                       Traceback (most recent call last)
+Cell In[50], line 1
+----> 1 import marginaleffects as me
+
+ModuleNotFoundError: No module named 'marginaleffects'
+
    +
    +

    Raw parameters#

    @@ -3112,8 +2351,50 @@

    Limitations of GLMs

    Exercises#

    -
    -

    Exercise 1: students pass or fail#

    +
    +

    Exercise 1: probabilities to odds and log-odds#

    +
    +
    +
    0.3/(1-0.3), 0.99/(1-0.99), 0.7/(1-0.7)
+
    +
    +
    +
    +
    (0.4285714285714286, 98.99999999999991, 2.333333333333333)
+
    +
    +
    +
    +
    +
    +
    logit(0.3), logit(0.99), logit(0.7)
+
    +
    +
    +
    +
    (-0.8472978603872036, 4.595119850134589, 0.8472978603872034)
+
    +
    +
    +
    +
    +
    +

    Exercise 2: log-odds to probabilities#

    +
    +
    +
    expit(-1), expit(1), expit(2)
+
    +
    +
    +
    +
    (0.2689414213699951, 0.7310585786300049, 0.8807970779778823)
+
    +
    +
    +
    +
    +
    +

    Exercise 3: students pass or fail#

    a) Load the dataset students.csv and add a column passing that contains 1 or 0, based on the above threshold score of 70.

    @@ -3184,8 +2465,8 @@

    Exercise 1: students pass or fail -

    Exercise 2: titanic survival data#

    +
    +

    Exercise 4: titanic survival data#

    Fit a logistic regression model that calculates the probability of survival for people who were on the Titanic, based on the data in datasets/exercises/titanic.csv. Use the variables age, sex, and pclass as predictors.

    cf. Titanic_Logistic_Regression.ipynb

    @@ -3244,8 +2525,8 @@

    Exercise 2: titanic survival data -

    Exercise 3: asthma attacks#

    +
    +

    Exercise 5: asthma attacks#

    Fit a Poisson regression model to the ../datasets/exercises/asthma.csv dataset.

    data source drkamarul/multivar_data_analysis

    @@ -3388,8 +2669,8 @@

    Exercise 3: asthma attackshttps://bookdown.org/drki_musa/dataanalysis/poisson-regression.html#multivariable-analysis-1

    -
    -

    Exercise 4: student admissions dataset#

    +
    +

    Exercise 6: student admissions dataset#

    The dataset datasets/exercises/binary.csv contains information about the acceptance decision for 400 students to a prestigious school. Try to fit a logistic regression model for the variable admit @@ -3500,8 +2781,8 @@

    Exercise 4: student admissions dataset -

    Exercise 5: ship accidents#

    +
    +

    Exercise 7: ship accidents#

    https://rdrr.io/cran/AER/man/ShipAccidents.html

    https://pages.stern.nyu.edu/~wgreene/Text/tables/tablelist5.htm

    https://pages.stern.nyu.edu/~wgreene/Text/tables/TableF21-3.txt

    @@ -3555,40 +2836,40 @@

    Bonus exercise A: honors classSo the model equation is

    \[ - \log(p/(1-p)) = \text{logit}(p) = -9.793942 + .1563404 \cdot \tt{math} + \log(p/(1-p)) = \texttt{logit}(p) = -9.793942 + .1563404 \cdot \texttt{math} \]
    @@ -3967,105 +3248,184 @@

    Bonus exercise: LA high schools (NOT A VERY GOOD FIT FOR POISSON MODEL)

    -
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    idgenderethnicschoolmathprlangprmathncelangncebilingdaysabs
    01001MHispanicAlpha633656.98883142.45085924
    11002MHispanicAlpha274437.09415846.82058724
    21003FHispanicAlpha203832.27545543.56657422
    31004FHispanicAlpha163829.05671743.56657423
    41005FHispanicAlpha2146.74804827.24847433
    -
    +
    ---------------------------------------------------------------------------
+gaierror                                  Traceback (most recent call last)
+File ~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:1346, in AbstractHTTPHandler.do_open(self, http_class, req, **http_conn_args)
+   1345 try:
+-> 1346     h.request(req.get_method(), req.selector, req.data, headers,
+   1347               encode_chunked=req.has_header('Transfer-encoding'))
+   1348 except OSError as err: # timeout error
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:1253, in HTTPConnection.request(self, method, url, body, headers, encode_chunked)
+   1252 """Send a complete request to the server."""
+-> 1253 self._send_request(method, url, body, headers, encode_chunked)
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:1299, in HTTPConnection._send_request(self, method, url, body, headers, encode_chunked)
+   1298     body = _encode(body, 'body')
+-> 1299 self.endheaders(body, encode_chunked=encode_chunked)
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:1248, in HTTPConnection.endheaders(self, message_body, encode_chunked)
+   1247     raise CannotSendHeader()
+-> 1248 self._send_output(message_body, encode_chunked=encode_chunked)
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:1008, in HTTPConnection._send_output(self, message_body, encode_chunked)
+   1007 del self._buffer[:]
+-> 1008 self.send(msg)
+   1010 if message_body is not None:
+   1011 
+   1012     # create a consistent interface to message_body
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:948, in HTTPConnection.send(self, data)
+    947 if self.auto_open:
+--> 948     self.connect()
+    949 else:
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:1415, in HTTPSConnection.connect(self)
+   1413 "Connect to a host on a given (SSL) port."
+-> 1415 super().connect()
+   1417 if self._tunnel_host:
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/http/client.py:919, in HTTPConnection.connect(self)
+    918 """Connect to the host and port specified in __init__."""
+--> 919 self.sock = self._create_connection(
+    920     (self.host,self.port), self.timeout, self.source_address)
+    921 self.sock.setsockopt(socket.IPPROTO_TCP, socket.TCP_NODELAY, 1)
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/socket.py:822, in create_connection(address, timeout, source_address)
+    821 err = None
+--> 822 for res in getaddrinfo(host, port, 0, SOCK_STREAM):
+    823     af, socktype, proto, canonname, sa = res
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/socket.py:953, in getaddrinfo(host, port, family, type, proto, flags)
+    952 addrlist = []
+--> 953 for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
+    954     af, socktype, proto, canonname, sa = res
+
+gaierror: [Errno 8] nodename nor servname provided, or not known
+
+During handling of the above exception, another exception occurred:
+
+URLError                                  Traceback (most recent call last)
+Cell In[102], line 1
+----> 1 lahigh_raw = pd.read_stata("https://stats.idre.ucla.edu/stat/stata/notes/lahigh.dta")
+      2 lahigh = lahigh_raw.convert_dtypes()
+      4 lahigh["gender"] = lahigh["gender"].astype(object).replace({1:"F", 2:"M"})
+
+File ~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/stata.py:2109, in read_stata(filepath_or_buffer, convert_dates, convert_categoricals, index_col, convert_missing, preserve_dtypes, columns, order_categoricals, chunksize, iterator, compression, storage_options)
+   2106     return reader
+   2108 with reader:
+-> 2109     return reader.read()
+
+File ~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/stata.py:1683, in StataReader.read(self, nrows, convert_dates, convert_categoricals, index_col, convert_missing, preserve_dtypes, columns, order_categoricals)
+   1671 @Appender(_read_method_doc)
+   1672 def read(
+   1673     self,
+   (...)
+   1681     order_categoricals: bool | None = None,
+   1682 ) -> DataFrame:
+-> 1683     self._ensure_open()
+   1685     # Handle options
+   1686     if convert_dates is None:
+
+File ~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/stata.py:1175, in StataReader._ensure_open(self)
+   1171 """
+   1172 Ensure the file has been opened and its header data read.
+   1173 """
+   1174 if not hasattr(self, "_path_or_buf"):
+-> 1175     self._open_file()
+
+File ~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/stata.py:1188, in StataReader._open_file(self)
+   1181 if not self._entered:
+   1182     warnings.warn(
+   1183         "StataReader is being used without using a context manager. "
+   1184         "Using StataReader as a context manager is the only supported method.",
+   1185         ResourceWarning,
+   1186         stacklevel=find_stack_level(),
+   1187     )
+-> 1188 handles = get_handle(
+   1189     self._original_path_or_buf,
+   1190     "rb",
+   1191     storage_options=self._storage_options,
+   1192     is_text=False,
+   1193     compression=self._compression,
+   1194 )
+   1195 if hasattr(handles.handle, "seekable") and handles.handle.seekable():
+   1196     # If the handle is directly seekable, use it without an extra copy.
+   1197     self._path_or_buf = handles.handle
+
+File ~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/common.py:728, in get_handle(path_or_buf, mode, encoding, compression, memory_map, is_text, errors, storage_options)
+    725     codecs.lookup_error(errors)
+    727 # open URLs
+--> 728 ioargs = _get_filepath_or_buffer(
+    729     path_or_buf,
+    730     encoding=encoding,
+    731     compression=compression,
+    732     mode=mode,
+    733     storage_options=storage_options,
+    734 )
+    736 handle = ioargs.filepath_or_buffer
+    737 handles: list[BaseBuffer]
+
+File ~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/common.py:384, in _get_filepath_or_buffer(filepath_or_buffer, encoding, compression, mode, storage_options)
+    382 # assuming storage_options is to be interpreted as headers
+    383 req_info = urllib.request.Request(filepath_or_buffer, headers=storage_options)
+--> 384 with urlopen(req_info) as req:
+    385     content_encoding = req.headers.get("Content-Encoding", None)
+    386     if content_encoding == "gzip":
+    387         # Override compression based on Content-Encoding header
+
+File ~/Projects/Minireference/STATSbook/noBSstatsnotebooks/venv/lib/python3.9/site-packages/pandas/io/common.py:289, in urlopen(*args, **kwargs)
+    283 """
+    284 Lazy-import wrapper for stdlib urlopen, as that imports a big chunk of
+    285 the stdlib.
+    286 """
+    287 import urllib.request
+--> 289 return urllib.request.urlopen(*args, **kwargs)
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:214, in urlopen(url, data, timeout, cafile, capath, cadefault, context)
+    212 else:
+    213     opener = _opener
+--> 214 return opener.open(url, data, timeout)
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:517, in OpenerDirector.open(self, fullurl, data, timeout)
+    514     req = meth(req)
+    516 sys.audit('urllib.Request', req.full_url, req.data, req.headers, req.get_method())
+--> 517 response = self._open(req, data)
+    519 # post-process response
+    520 meth_name = protocol+"_response"
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:534, in OpenerDirector._open(self, req, data)
+    531     return result
+    533 protocol = req.type
+--> 534 result = self._call_chain(self.handle_open, protocol, protocol +
+    535                           '_open', req)
+    536 if result:
+    537     return result
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:494, in OpenerDirector._call_chain(self, chain, kind, meth_name, *args)
+    492 for handler in handlers:
+    493     func = getattr(handler, meth_name)
+--> 494     result = func(*args)
+    495     if result is not None:
+    496         return result
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:1389, in HTTPSHandler.https_open(self, req)
+   1388 def https_open(self, req):
+-> 1389     return self.do_open(http.client.HTTPSConnection, req,
+   1390         context=self._context, check_hostname=self._check_hostname)
+
+File ~/.pyenv/versions/3.9.4/lib/python3.9/urllib/request.py:1349, in AbstractHTTPHandler.do_open(self, http_class, req, **http_conn_args)
+   1346         h.request(req.get_method(), req.selector, req.data, headers,
+   1347                   encode_chunked=req.has_header('Transfer-encoding'))
+   1348     except OSError as err: # timeout error
+-> 1349         raise URLError(err)
+   1350     r = h.getresponse()
+   1351 except:
+
+URLError: <urlopen error [Errno 8] nodename nor servname provided, or not known>
+
    +
    +

    @@ -4075,20 +3435,6 @@

    Bonus exercise: LA high schools (NOT A VERY GOOD FIT FOR POISSON MODEL)

    -
    -
    Optimization terminated successfully.
-         Current function value: 4.898642
-         Iterations 5
-
    -
    -
    Intercept         2.687666
-C(gender)[T.M]   -0.400921
-mathnce          -0.003523
-langnce          -0.012152
-dtype: float64
-
    -
    -
    @@ -4097,14 +3443,6 @@

    Bonus exercise: LA high schools (NOT A VERY GOOD FIT FOR POISSON MODEL)

    -
    -
    C(gender)[T.M]    0.669703
-mathnce           0.996483
-langnce           0.987921
-dtype: float64
-
    -
    -
    @@ -4113,13 +3451,6 @@

    Bonus exercise: LA high schools (NOT A VERY GOOD FIT FOR POISSON MODEL)

    -
    -
    0    0.609079
-1    0.736361
-Name: C(gender)[T.M], dtype: float64
-
    -
    -
    @@ -4160,20 +3491,6 @@

    Diagnostics -
    Optimization terminated successfully.
-         Current function value: 4.898642
-         Iterations 5
-
    -
    -
    Intercept                       2.286745
-C(gender, Treatment(1))[T.F]    0.400921
-mathnce                        -0.003523
-langnce                        -0.012152
-dtype: float64
-
    -
    -

    @@ -4309,11 +3626,13 @@

    Links#
  • Exercises
  • Bonus Exercises
      diff --git a/notebooks/50_extra_bayesian_stuff.html b/notebooks/50_extra_bayesian_stuff.html new file mode 100644 index 00000000..f006d467 --- /dev/null +++ b/notebooks/50_extra_bayesian_stuff.html @@ -0,0 +1,779 @@ + + + + + + + + + + + + Chapter 5: Extra code, drafts, and cut material — No BS Stats Notebooks + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + + + + + + + + + + + +
      +
      +
      +
      + + + Ctrl+K +
      +
      + + + +
      +
      + +
      + + + +
      + + + + +
      + +
      +
      + + + +
      +
      +
      + + +
      +
      + + + + +
      + +
      + + + +
      + +
      +
      + +
      +
      + +
      + +
      + +
      + + +
      + +
      + +
      + + + + + +
      + + +
      + + + + + + +
      + + +
      + + + + + + +
      + + +
      + + + + + + + + + + + + + +
      + +
      + +
      +
      + + + +
      +

      Chapter 5: Extra code, drafts, and cut material

      + +
      +
      + +
      +

      Contents

      +
      + +
      +
      +
      + + + + +
      + +
      +

      Chapter 5: Extra code, drafts, and cut material#

      +
      +

      Bayesian p-value#

      +
      +
      +
      import pymc as pm
+import numpy as np
+import arviz as az
+
+# Simulated data
+np.random.seed(42)
+x = np.random.normal(0, 1, 100)
+y = 3 + 2 * x + np.random.normal(0, 1, 100)
+
+# Bayesian Linear Regression Model
+with pm.Model() as model:
+    # Priors
+    beta0 = pm.Normal("beta0", mu=0, sigma=10)
+    beta1 = pm.Normal("beta1", mu=0, sigma=10)
+    sigma = pm.HalfNormal("sigma", sigma=1)
+    
+    # Likelihood
+    mu = beta0 + beta1 * x
+    y_obs = pm.Normal("y_obs", mu=mu, sigma=sigma, observed=y)
+    
+    # Sampling
+    trace = pm.sample(2000, return_inferencedata=True)
+
      +
      +
      +
      +
      Auto-assigning NUTS sampler...
+
      +
      +
      Initializing NUTS using jitter+adapt_diag...
+
      +
      +
      Multiprocess sampling (2 chains in 2 jobs)
+
      +
      +
      NUTS: [beta0, beta1, sigma]
+
      +
      +
      + +
      +
      + + 2.22% [133/6000 00:00<00:03 Sampling 2 chains, 0 divergences] +
      + 
      ---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Cell In[1], line 22
+     19 y_obs = pm.Normal("y_obs", mu=mu, sigma=sigma, observed=y)
+     21 # Sampling
+---> 22 trace = pm.sample(2000, return_inferencedata=True)
+
+File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pymc/sampling/mcmc.py:791, in sample(draws, tune, chains, cores, random_seed, progressbar, step, nuts_sampler, initvals, init, jitter_max_retries, n_init, trace, discard_tuned_samples, compute_convergence_checks, keep_warning_stat, return_inferencedata, idata_kwargs, nuts_sampler_kwargs, callback, mp_ctx, model, **kwargs)
+    787 t_sampling = time.time() - t_start
+    789 # Packaging, validating and returning the result was extracted
+    790 # into a function to make it easier to test and refactor.
+--> 791 return _sample_return(
+    792     run=run,
+    793     traces=traces,
+    794     tune=tune,
+    795     t_sampling=t_sampling,
+    796     discard_tuned_samples=discard_tuned_samples,
+    797     compute_convergence_checks=compute_convergence_checks,
+    798     return_inferencedata=return_inferencedata,
+    799     keep_warning_stat=keep_warning_stat,
+    800     idata_kwargs=idata_kwargs or {},
+    801     model=model,
+    802 )
+
+File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pymc/sampling/mcmc.py:822, in _sample_return(run, traces, tune, t_sampling, discard_tuned_samples, compute_convergence_checks, return_inferencedata, keep_warning_stat, idata_kwargs, model)
+    820 # Pick and slice chains to keep the maximum number of samples
+    821 if discard_tuned_samples:
+--> 822     traces, length = _choose_chains(traces, tune)
+    823 else:
+    824     traces, length = _choose_chains(traces, 0)
+
+File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pymc/backends/base.py:601, in _choose_chains(traces, tune)
+    599 lengths = [max(0, len(trace) - tune) for trace in traces]
+    600 if not sum(lengths):
+--> 601     raise ValueError("Not enough samples to build a trace.")
+    603 idxs = np.argsort(lengths)
+    604 l_sort = np.array(lengths)[idxs]
+
+ValueError: Not enough samples to build a trace.
+
      +
      +
      +
      +
      +
      +
      # Posterior Predictive Check
+# with model:
+#     ppc = pm.sample_posterior_predictive(trace)    
+# Posterior Predictive Check
+ppc = pm.sample_posterior_predictive(trace, model=model)
+    
+
      +
      +
      +
      +
      Sampling: [y_obs]
+
      +
      +
      + +
      +
      + + 100.00% [8000/8000 00:00<00:00] +
      +
      +
      +
      +
      +
      # Extract the posterior predictive samples for 'y_obs'
+y_rep = ppc.posterior_predictive["y_obs"].values
+
+# Calculate Bayesian p-value for the slope
+test_stat_observed = np.mean(y)  # Example test statistic
+test_stat_rep = np.mean(y_rep, axis=1)
+bayesian_p_value = np.mean(test_stat_rep >= test_stat_observed)
+print("Bayesian p-value:", bayesian_p_value)
+
      +
      +
      +
      +
      Bayesian p-value: 0.4925
+
      +
      +
      +
      +
      +
      + + + + +
      + + + + + + +
      + +
      +
      +
      + +
      + + + +
      + +
      +
      + Contents +
      +
      + +
      + + +
      +
      + +
      + +
      + +

      +By Ivan Savov +

      + +
      + +
      + + +

      + + © Copyright 2023. +
      + +

      + +
      + +
      + +
      + +
      + +
      + +
      +
      + + +
      +
      +
      + + + + + +
      +
      + + \ No newline at end of file diff --git a/notebooks/51_intro_to_Bayesian_stats.html b/notebooks/51_intro_to_Bayesian_stats.html new file mode 100644 index 00000000..d54c58fc --- /dev/null +++ b/notebooks/51_intro_to_Bayesian_stats.html @@ -0,0 +1,932 @@ + + + + + + + + + + + + Section 5.1 — Introduction to Bayesian statistics — No BS Stats Notebooks + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + + + + + + + + + + + +
      +
      +
      +
      + + + Ctrl+K +
      +
      + + + +
      +
      + +
      + + + +
      + + + + +
      + +
      +
      + + + +
      +
      +
      + + +
      +
      + + + + +
      + +
      + + + +
      + +
      +
      + +
      +
      + +
      + +
      + +
      + + +
      + +
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      + + + + + +
      + + +
      + + + + + + +
      + + +
      + + + + + + +
      + + +
      + + + + + + + + + + + + + +
      + +
      + +
      +
      + + + +
      +

      Section 5.1 — Introduction to Bayesian statistics

      + +
      + +
      +
      + + + + +
      + +
      +

      Section 5.1 — Introduction to Bayesian statistics#

      +

      This notebook contains the code examples from Section 5.1 Introduction to Bayesian statistics from the No Bullshit Guide to Statistics.

      +
      +

      Notebook setup#

      +
      +
      +
      # load Python modules
+import os
+import numpy as np
+import pandas as pd
+import seaborn as sns
+import matplotlib.pyplot as plt
+
      +
      +
      +
      +
      +
      +
      # Figures setup
+plt.clf()  # needed otherwise `sns.set_theme` doesn"t work
+from plot_helpers import RCPARAMS
+RCPARAMS.update({"figure.figsize": (5, 3)})   # good for screen
+# RCPARAMS.update({"figure.figsize": (5, 1.6)})  # good for print
+sns.set_theme(
+    context="paper",
+    style="whitegrid",
+    palette="colorblind",
+    rc=RCPARAMS,
+)
+
+# High-resolution please
+%config InlineBackend.figure_format = "retina"
+
+# Where to store figures
+DESTDIR = "figures/bayesian/intro"
+
      +
      +
      +
      +
      <Figure size 640x480 with 0 Axes>
+
      +
      +
      +
      +
      +
      +
      # set random seed for repeatability
+np.random.seed(42)
+#######################################################
+
      +
      +
      +
      +
      +
      +
      # via https://nbviewer.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers
+# /blob/master/Chapter1_Introduction/Ch1_Introduction_PyMC3.ipynb
+from scipy.stats import beta
+from scipy.stats import bernoulli
+
+n_trials = [0, 1, 2, 3, 4, 5, 8, 15, 50, 500]
+data = bernoulli.rvs(0.5, size=n_trials[-1])
+x = np.linspace(0, 1, 100)
+
+# For the already prepared, I'm using Binomial's conj. prior.
+for k, N in enumerate(n_trials):
+    sx = plt.subplot(len(n_trials)//2, 2, k+1)
+    plt.xlabel("$p$, probability of heads") \
+        if k in [0, len(n_trials)-1] else None
+    plt.setp(sx.get_yticklabels(), visible=False)
+    heads = data[:N].sum()
+    y = beta.pdf(x, 1 + heads, 1 + N - heads)
+    plt.plot(x, y, label="observe %d tosses,\n %d heads" % (N, heads))
+    plt.fill_between(x, 0, y, color="#348ABD", alpha=0.4)
+    plt.vlines(0.5, 0, 4, color="k", linestyles="--", lw=1)
+
+    leg = plt.legend()
+    leg.get_frame().set_alpha(0.4)
+    plt.autoscale(tight=True)
+
+
+plt.suptitle("Bayesian updating of posterior probabilities",
+             y=1.02,
+             fontsize=14);
+
      +
      +
      +
      +../_images/193d8b4f98ddb39473f3be68613bbc19c5b61c184e042e365b5f87ac3afadcd9.png +
      +
      +
      +
      +

      Example 1: estimating the probability of a biased coin#

      +
      +
      +
      from scipy.special import binom, betaln
+
+def beta_binom(prior, y):
+    """
+    Compute the marginal-log-likelihood for a beta-binomial model,
+    analytically.
+
+    prior : tuple
+        tuple of alpha and beta parameter for the prior (beta distribution)
+    y : array
+        array with "1" and "0" corresponding to the success and fails respectively
+    """
+    α, β = prior
+    success = np.sum(y)
+    trials = len(y)
+    return np.log(binom(trials, success)) + betaln(α + success, β+trials-success) - betaln(α, β)
+
      +
      +
      +
      +
      +
      +
      from scipy import stats
+
+
+def beta_binom_harmonic(prior, y, s=10000):
+    """
+    Compute the marginal-log-likelihood for a beta-binomial model,
+    using the harmonic mean estimator.
+
+    prior : tuple
+        tuple of alpha and beta parameter for the prior (beta distribution)
+    y : array
+        array with "1" and "0" corresponding to the success and fails respectively
+    s : int
+        number of samples from the posterior
+    """
+    α, β = prior
+    success = np.sum(y)
+    trials = len(y)
+    posterior_samples = stats.beta(α + success, β+trials-success).rvs(s)
+    log_likelihood = stats.binom.logpmf(success, trials, posterior_samples)
+    return 1/np.mean(1/log_likelihood)
+
      +
      +
      +
      +
      +
      +
      data = [np.repeat([1, 0], rep)
+        for rep in ((1, 0), (1, 1), (5, 5), (100, 100))]
+priors = ((1, 1), (100, 100), (1, 2), (1, 200))
+
+x_names = [repr((sum(x), len(x)-sum(x))) for x in data]
+y_names = ["Beta" + repr(x) for x in priors]
+
+fig, ax = plt.subplots()
+error_matrix = np.zeros((len(priors), len(data)))
+for i, prior in enumerate(priors):
+    for j, y in enumerate(data):
+        error_matrix[i, j] = 100 * \
+            (1 - (beta_binom_harmonic(prior, y) / beta_binom(prior, y)))
+im = ax.imshow(error_matrix, cmap='viridis')
+ax.set_xticks(np.arange(len(x_names)))
+ax.set_yticks(np.arange(len(y_names)))
+ax.set_xticklabels(x_names)
+ax.set_yticklabels(y_names)
+fig.colorbar(im)
+# plt.savefig("img/chp11/harmonic_mean_heatmap.png")
+
      +
      +
      +
      +
      <matplotlib.colorbar.Colorbar at 0x7fb5ef3f55b0>
+
      +
      +../_images/d3d691c99f489baeb4ffd5ab63652dfe9a4c7a6d103841d9e39f77892f3a5ec3.png +
      +
      +
      +
      +
      def normal_harmonic(sd_0, sd_1, y, s=10000):
+    post_tau = 1/sd_0**2 + 1/sd_1**2
+    posterior_samples = stats.norm(loc=(y/sd_1**2)/post_tau, scale=(1/post_tau)**0.5).rvs((s, len(x)))
+    log_likelihood = stats.norm.logpdf(loc=x, scale=sd_1, x=posterior_samples).sum(1)
+    return 1/np.mean(1/log_likelihood)
+
      +
      +
      +
      +
      +
      +
      σ_0 = 1
+σ_1 = 1
+y = np.array([0])
+stats.norm.logpdf(loc=0, scale=(σ_0**2+σ_1**2)**0.5, x=y).sum()
+
      +
      +
      +
      +
      -1.2655121234846454
+
      +
      +
      +
      +
      +
      +
      def posterior_ml_ic_normal(σ_0=1, σ_1=1, y=[1]):
+    n = len(y)
+    var_μ = 1/((1/σ_0**2) + (n/σ_1**2))
+    μ = var_μ * np.sum(y)/σ_1**2
+    σ_μ = var_μ**0.5
+
+    posterior = stats.norm(loc=μ, scale=σ_μ)
+    samples = posterior.rvs(size=(2, 1000))
+    log_likelihood = stats.norm(loc=samples[:, :, None], scale=σ_1).logpdf(y)
+    idata = az.from_dict(log_likelihood={'o': log_likelihood})
+
+    log_ml = stats.norm.logpdf(loc=0, scale=(σ_0**2+σ_1**2)**0.5, x=y).sum()
+    
+    x = np.linspace(-5, 6, 300)
+    density = posterior.pdf(x)
+    
+    return μ, σ_μ, x, density, log_ml, az.waic(idata).elpd_waic, az.loo(idata, reff=1).elpd_loo
+
      +
      +
      +
      +
      +
      +
      import arviz as az
+
+y = np.array([ 0.65225338, -0.06122589,  0.27745188,  1.38026371, -0.72751008,
+              -1.10323829,  2.07122286, -0.52652711,  0.51528113,  0.71297661])
+
+_, ax = plt.subplots(3, figsize=(10, 6), sharex=True, sharey=True,
+                     constrained_layout=True)
+
+for i, σ_0 in enumerate((1, 10, 100)):
+    μ_μ, σ_μ, x, density, log_ml, waic, loo = posterior_ml_ic_normal(σ_0, σ_1, y)
+    ax[i].plot(x, stats.norm(loc=0, scale=(σ_0**2+σ_1**2)**0.5).pdf(x), lw=2)
+    ax[i].plot(x, density, lw=2, color='C4')
+    ax[i].plot(0, label=f'log_ml {log_ml:.1f}\nwaic {waic:.1f}\nloo {loo:.1f}\n', alpha=0)
+    ax[i].set_title(f'μ_μ={μ_μ:.2f} σ_μ={σ_μ:.2f}')
+    ax[i].legend()
+ax[2].set_yticks([])
+
+ax[2].set_xlabel("μ")
+
+#plt.savefig("img/chp11/ml_waic_loo.png")
+
      +
      +
      +
      +
      Text(0.5, 0, 'μ')
+
      +
      +../_images/336e553b1e15c6958c59d00722972a35abb626fae85ff3523b0a40d5ca975f06.png +
      +
      +
      +
      +
      σ_0 = 1
+σ_1 = 1
+y = np.array([0])
+stats.norm.logpdf(loc=0, scale=(σ_0**2 + σ_1**2)**0.5, x=y).sum()
+
      +
      +
      +
      +
      -1.2655121234846454
+
      +
      +
      +
      +
      +
      +
      N = 10000
+x, y = np.random.uniform(-1, 1, size=(2, N))
+inside = (x**2 + y**2) <= 1
+pi = inside.sum()*4/N
+error = abs((pi - np.pi) / pi) * 100
+
      +
      +
      +
      +
      +
      +
      total = 100000
+
+dims = []
+prop = []
+for d in range(2, 15):
+    x = np.random.random(size=(d, total))
+    inside = ((x * x).sum(axis=0) < 1).sum()
+    dims.append(d)
+    prop.append(inside / total)
+    
+plt.plot(dims, prop);
+
      +
      +
      +
      +../_images/93b781a05ec28ddc6351a24c5908f716ae99a7f6e8fada7880c48a265bf78c90.png +
      +
      +
      +
      +
      def posterior_grid(ngrid=10, α=1, β=1, heads=6, trials=9):
+    grid = np.linspace(0, 1, ngrid)
+    prior = stats.beta(α, β).pdf(grid)
+    likelihood = stats.binom.pmf(heads, trials, grid)
+    posterior = likelihood * prior
+    posterior /= posterior.sum()
+    return posterior
+
      +
      +
      +
      +
      +
      + + + + +
      + + + + + + +
      + +
      +
      +
      + +
      + + + +
      + +
      +
      + Contents +
      +
      + +
      + + +
      +
      + +
      + +
      + +

      +By Ivan Savov +

      + +
      + +
      + + +

      + + © Copyright 2023. +
      + +

      + +
      + +
      + +
      + +
      + +
      + +
      +
      + + +
      +
      +
      + + + + + +
      +
      + + \ No newline at end of file diff --git a/notebooks/52_Bayesian_inference_computations.html b/notebooks/52_Bayesian_inference_computations.html new file mode 100644 index 00000000..f941d047 --- /dev/null +++ b/notebooks/52_Bayesian_inference_computations.html @@ -0,0 +1,956 @@ + + + + + + + + + + + + Section 5.2 — Bayesian inference computations — No BS Stats Notebooks + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + + + + + + + + + + + +
      +
      +
      +
      + + + Ctrl+K +
      +
      + + + +
      +
      + +
      + + + +
      + + + + +
      + +
      +
      + + + +
      +
      +
      + + +
      +
      + + + + +
      + +
      + + + +
      + +
      +
      + +
      +
      + +
      + +
      + +
      + + +
      + +
      + +
      + + + + + +
      + + +
      + + + + + + +
      + + +
      + + + + + + +
      + + +
      + + + + + + + + + + + + + +
      + +
      + +
      +
      + + + +
      +

      Section 5.2 — Bayesian inference computations

      + +
      + +
      +
      + + + + +
      + +
      +

      Section 5.2 — Bayesian inference computations#

      +

      This notebook contains the code examples from Section 5.2 Bayesian inference computations from the No Bullshit Guide to Statistics.

      +
      +

      Notebook setup#

      +
      +
      +
      # load Python modules
+import os
+import numpy as np
+import pandas as pd
+import seaborn as sns
+import matplotlib.pyplot as plt
+
      +
      +
      +
      +
      +
      +
      # Figures setup
+plt.clf()  # needed otherwise `sns.set_theme` doesn"t work
+from plot_helpers import RCPARAMS
+RCPARAMS.update({"figure.figsize": (5, 3)})   # good for screen
+# RCPARAMS.update({"figure.figsize": (5, 1.6)})  # good for print
+sns.set_theme(
+    context="paper",
+    style="whitegrid",
+    palette="colorblind",
+    rc=RCPARAMS,
+)
+
+# High-resolution please
+%config InlineBackend.figure_format = "retina"
+
+# Where to store figures
+DESTDIR = "figures/bayesian/computations"
+
      +
      +
      +
      +
      <Figure size 640x480 with 0 Axes>
+
      +
      +
      +
      +
      +
      +
      # set random seed for repeatability
+np.random.seed(42)
+#######################################################
+
      +
      +
      +
      +
      +
      +

      Example 1: estimating the probability of a biased coin#

      +
      +
      +
      from scipy.stats import bernoulli
+tosses = bernoulli(0.7).rvs(20)
+
      +
      +
      +
      +
      +
      +
      # Declare a model in PyMC
+
+import pymc as pm
+
+with pm.Model() as model:
+    # Specify the prior distribution of unknown parameter
+    p = pm.Beta("p", alpha=1, beta=1)
+
+    # Specify the likelihood distribution and condition on the observed data
+    y_obs = pm.Binomial("y_obs", n=1, p=p, observed=tosses)
+
+    # Sample from the posterior distribution
+    idata = pm.sample(1000)
+
      +
      +
      +
      +
      Auto-assigning NUTS sampler...
+
      +
      +
      Initializing NUTS using jitter+adapt_diag...
+
      +
      +
      Multiprocess sampling (2 chains in 2 jobs)
+
      +
      +
      NUTS: [p]
+
      +
      +
      + +
      +
      + + 100.00% [4000/4000 00:01<00:00 Sampling 2 chains, 0 divergences] +
      + 
      Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 1 seconds.
+
      +
      +
      We recommend running at least 4 chains for robust computation of convergence diagnostics
+
      +
      +
      +
      +
      +
      +
      import arviz as az
+az.summary(idata)
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      meansdhdi_3%hdi_97%mcse_meanmcse_sdess_bulkess_tailr_hat
      p0.6840.0990.5130.8680.0030.002862.01304.01.0
      +
      +
      +
      +
      +
      pred_dists = (pm.sample_prior_predictive(1000, model).prior_predictive["y_obs"].values,
+              pm.sample_posterior_predictive(idata, model).posterior_predictive["y_obs"].values)
+
      +
      +
      +
      +
      Sampling: [p, y_obs]
+
      +
      +
      Sampling: [y_obs]
+
      +
      +
      + +
      +
      + + 100.00% [2000/2000 00:00<00:00] +
      +
      +
      +
      +
      +
      fig, axes = plt.subplots(4, 1, figsize=(9, 9))
+
+for idx, n_d, dist in zip((1, 3), ("Prior", "Posterior"), pred_dists):
+    az.plot_dist(dist.sum(-1), 
+                 hist_kwargs={"color":"0.5", "bins":range(0, 22)},
+                 ax=axes[idx])
+    axes[idx].set_title(f"{n_d} predictive distribution", fontweight='bold')
+    axes[idx].set_xlim(-1, 21)
+    axes[idx].set_ylim(0, 0.15)
+    axes[idx].set_xlabel("number of success")
+
+az.plot_dist(pm.draw(p, 1000),
+             plot_kwargs={"color":"0.5"},
+             fill_kwargs={'alpha':1}, ax=axes[0])
+axes[0].set_title("Prior distribution", fontweight='bold')
+axes[0].set_xlim(0, 1)
+axes[0].set_ylim(0, 4)
+axes[0].tick_params(axis='both', pad=7)
+axes[0].set_xlabel("p")
+
+az.plot_dist(idata.posterior["p"],
+             plot_kwargs={"color":"0.5"},
+             fill_kwargs={'alpha':1},
+             ax=axes[2])
+axes[2].set_title("Posterior distribution", fontweight='bold')
+axes[2].set_xlim(0, 1)
+axes[2].set_ylim(0, 5)
+axes[2].tick_params(axis='both', pad=7)
+axes[2].set_xlabel("p");
+
      +
      +
      +
      +../_images/1dfd788426c9ce57e6cda198a3dd9423e8494c49e0716c01c5bb02d8d4873750.png +
      +
      +
      +
      +
      from scipy.stats import binom
+
+predictions = (binom(n=1, p=idata.posterior["p"].mean()).rvs((4000, len(tosses))),
+               pred_dists[1])
+
+for d, c, l in zip(predictions, ("C0", "C4"), ("posterior mean", "posterior predictive")):
+    ax = az.plot_dist(d.sum(-1),
+                      label=l,
+                      figsize=(10, 5),
+                      hist_kwargs={"alpha": 0.5, "color":c, "bins":range(0, 22)})
+    ax.set_yticks([])
+    ax.set_xlabel("number of success")
+
      +
      +
      +
      +../_images/aa554fd940665088ca108d40500d3437e7d882788ae25b3dc1652c11a54d6f04.png +
      +
      +
      +
      +

      Discussion#

      +
      +

      MCMC diagnostic plots#

      +

      There are several Arviz plots we can use to check if the Markov Chain Monte Carlo chains were sampling from the posterior as expected, or …

      +
      +
      +
      # az.plot_trace(idata);
+# az.plot_trace(idata, kind="rank_bars");
+# az.plot_trace(idata, kind="rank_vlines");
+
+# plot_cap ~= partial regression plots?
+# e.g. plot_cap(model_2, fitted_2, "weight", ax=ax);
+
      +
      +
      +
      +
      +
      +

      Choice of priors#

      +

      Different priors lead to different posteriors.

      +

      See Code 1.8 and Figure 1.7 in +chp_01.ipynb

      +
      +
      +
      from scipy.stats import beta
+
+x = np.linspace(0, 1, 500)
+params = [(0.5, 0.5), (1, 1), (3,3), (100, 25)]
+
+labels = ["Jeffreys", "MaxEnt", "Weakly  Informative",
+          "Informative"]
+
+_, ax = plt.subplots()
+for (α, β), label, c in zip(params, labels, (0, 1, 4, 2)):
+    pdf = beta.pdf(x, α, β)
+    ax.plot(x, pdf, label=f"{label}", c=f"C{c}", lw=3)
+    ax.set(yticks=[], xlabel="θ", title="Priors")
+    ax.legend()
+# plt.savefig("img/chp01/prior_informativeness_spectrum.png")
+
      +
      +
      +
      +../_images/1653eb3ef0ddc25899b3197f96e7367594c4fe180aafd76872786fb91d873f5c.png +
      +
      +
      +
      +

      Bayesian workflow#

      +

      See also chp_09.ipynb

      +
      +
      +
      + + + + +
      + + + + + + +
      + +
      +
      +
      + +
      + + + +
      + +
      +
      + Contents +
      +
      + +
      + + +
      +
      + +
      + +
      + +

      +By Ivan Savov +

      + +
      + +
      + + +

      + + © Copyright 2023. +
      + +

      + +
      + +
      + +
      + +
      + +
      + +
      +
      + + +
      +
      +
      + + + + + +
      +
      + + \ No newline at end of file diff --git a/notebooks/53_difference_between_means.html b/notebooks/53_difference_between_means.html new file mode 100644 index 00000000..03710926 --- /dev/null +++ b/notebooks/53_difference_between_means.html @@ -0,0 +1,2533 @@ + + + + + + + + + + + + Section 5.3 — Bayesian difference between means — No BS Stats Notebooks + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + + + + + + + + + + + +
      +
      +
      +
      + + + Ctrl+K +
      +
      + + + +
      +
      + +
      + + + +
      + + + + +
      + +
      +
      + + + +
      +
      +
      + + +
      +
      + + + + +
      + +
      + + + +
      + +
      +
      + +
      +
      + +
      + +
      + +
      + + +
      + +
      + +
      + + + + + +
      + + +
      + + + + + + +
      + + +
      + + + + + + +
      + + +
      + + + + + + + + + + + + + +
      + +
      + +
      +
      + + + +
      +

      Section 5.3 — Bayesian difference between means

      + +
      + +
      +
      + + + + +
      + +
      +

      Section 5.3 — Bayesian difference between means#

      +

      This notebook contains the code examples from Section 5.3 Bayesian difference between means from the No Bullshit Guide to Statistics.

      +

      See also t-test.ipynb

      +
      +

      Notebook setup#

      +
      +
      +
      # load Python modules
+import os
+import numpy as np
+import pandas as pd
+import seaborn as sns
+import matplotlib.pyplot as plt
+
      +
      +
      +
      +
      +
      +
      # Figures setup
+plt.clf()  # needed otherwise `sns.set_theme` doesn"t work
+from plot_helpers import RCPARAMS
+RCPARAMS.update({"figure.figsize": (5, 3)})   # good for screen
+# RCPARAMS.update({"figure.figsize": (5, 1.6)})  # good for print
+sns.set_theme(
+    context="paper",
+    style="whitegrid",
+    palette="colorblind",
+    rc=RCPARAMS,
+)
+
+# High-resolution please
+%config InlineBackend.figure_format = "retina"
+
+# Where to store figures
+DESTDIR = "figures/bayesian/dmeans"
+
      +
      +
      +
      +
      <Figure size 640x480 with 0 Axes>
+
      +
      +
      +
      +
      +
      +
      # set random seed for repeatability
+np.random.seed(42)
+#######################################################
+
      +
      +
      +
      +
      +
      +

      Example movies genres#

      +

      see https://www.andrewheiss.com/blog/2019/01/29/diff-means-half-dozen-ways/

      +

      see also https://bookdown.org/content/3686/metric-predicted-variable-on-one-or-two-groups.html#two-groups

      +
      +
      +
      movies = pd.read_csv("../datasets/movies.csv")
+movies.head()
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      titleyearratinggenregenre_numeric
      0Blowing Wild19535.6Action1
      1No Way Back19955.2Action1
      2New Jack City19916.1Action1
      3Noigwon19834.2Action1
      4Tarzan and the Jungle Boy19685.2Action1
      +
      +
      +
      +
      +
      movies.groupby("genre")["rating"].mean()
+
      +
      +
      +
      +
      genre
+Action    5.2845
+Comedy    5.9670
+Name: rating, dtype: float64
+
      +
      +
      +
      +
      +
      +
      from scipy.stats import ttest_ind
+
+actions = movies[movies["genre"]=="Action"]["rating"]
+comedies = movies[movies["genre"]=="Comedy"]["rating"]
+
+ttest_ind(actions, comedies, equal_var=True)
+
      +
      +
      +
      +
      Ttest_indResult(statistic=-4.47525173500199, pvalue=9.976981171112132e-06)
+
      +
      +
      +
      +
      +
      +
      ttest_ind(actions, comedies, equal_var=False)
+
      +
      +
      +
      +
      Ttest_indResult(statistic=-4.47525173500199, pvalue=9.978285839671782e-06)
+
      +
      +
      +
      +
      +
      +
      import bambi as bmb
+
      +
      +
      +
      +
      +
      +
      # Model formula
+levels = ["Comedy", "Action"]
+formula = bmb.Formula("rating ~ 1 + C(genre, levels=levels)")
+
+# Choose custom priors 
+priors = {
+    "Intercept": bmb.Prior("Normal", mu=0, sigma=5),
+    "C(genre, levels=levels)": bmb.Prior("Normal", mu=0, sigma=1)
+}
+
+# Build model
+model_eq = bmb.Model(formula, priors=priors, data=movies)
+
+# Get model description
+print(model_eq)
+
      +
      +
      +
      +
             Formula: rating ~ 1 + C(genre, levels=levels)
+        Family: gaussian
+          Link: mu = identity
+  Observations: 400
+        Priors: 
+    target = mu
+        Common-level effects
+            Intercept ~ Normal(mu: 0.0, sigma: 5.0)
+            C(genre, levels=levels) ~ Normal(mu: 0.0, sigma: 1.0)
+        
+        Auxiliary parameters
+            sigma ~ HalfStudentT(nu: 4.0, sigma: 1.559)
+
      +
      +
      +
      +
      +
      +
      # model_eq.build()
+# model_eq.graph()
+
      +
      +
      +
      +
      +
      +
      # Fit the model using 1000 on each chain
+idata_eq = model_eq.fit(draws=1000)
+
      +
      +
      +
      +
      Auto-assigning NUTS sampler...
+
      +
      +
      Initializing NUTS using jitter+adapt_diag...
+
      +
      +
      Multiprocess sampling (2 chains in 2 jobs)
+
      +
      +
      NUTS: [rating_sigma, Intercept, C(genre, levels=levels)]
+
      +
      +
      + +
      +
      + + 100.00% [4000/4000 00:02<00:00 Sampling 2 chains, 0 divergences] +
      + 
      Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 2 seconds.
+
      +
      +
      We recommend running at least 4 chains for robust computation of convergence diagnostics
+
      +
      +
      +
      +
      +
      +
      import arviz as az
+az.summary(idata_eq, stat_focus="median")
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      medianmadeti_3%eti_97%mcse_medianess_medianess_tailr_hat
      Intercept5.9590.0705.7586.1590.0032891.1531635.01.0
      C(genre, levels=levels)[Action]-0.6630.101-0.961-0.3620.0042584.1641335.01.0
      rating_sigma1.5270.0381.4291.6290.0012429.4511399.01.0
      +
      +
      +
      +

      Regression, assuming unequal variances#

      +
      +
      +
      levels = ["Comedy", "Action"]
+formula_uneq = bmb.Formula("rating ~ 1 + C(genre,levels=levels)", "sigma ~ C(genre,levels=levels)")
+
+priors = {
+    "Intercept": bmb.Prior("Normal", mu=0, sigma=5),
+    "C(genre, levels=levels)": bmb.Prior("Normal", mu=0, sigma=1),
+    "sigma": {"C(genre, levels=levels)": bmb.Prior("Cauchy", alpha=0, beta=1)},
+}
+
+# Build model
+model_uneq = bmb.Model(formula_uneq, priors=priors, data=movies)
+
+# Get model description
+print(model_uneq)
+# model_uneq.build()
+# model_uneq.graph()
+
      +
      +
      +
      +
             Formula: rating ~ 1 + C(genre,levels=levels)
+                sigma ~ C(genre,levels=levels)
+        Family: gaussian
+          Link: mu = identity
+                sigma = log
+  Observations: 400
+        Priors: 
+    target = mu
+        Common-level effects
+            Intercept ~ Normal(mu: 0.0, sigma: 5.0)
+            C(genre, levels=levels) ~ Normal(mu: 0.0, sigma: 1.0)
+    target = sigma
+        Common-level effects
+            sigma_Intercept ~ Normal(mu: 0.0, sigma: 1.0)
+            sigma_C(genre, levels=levels) ~ Cauchy(alpha: 0.0, beta: 1.0)
+
      +
      +
      +
      +
      +
      +
      idata_uneq = model_uneq.fit(draws=1000)
+
      +
      +
      +
      +
      Auto-assigning NUTS sampler...
+
      +
      +
      Initializing NUTS using jitter+adapt_diag...
+
      +
      +
      Multiprocess sampling (2 chains in 2 jobs)
+
      +
      +
      NUTS: [Intercept, C(genre, levels=levels), sigma_Intercept, sigma_C(genre, levels=levels)]
+
      +
      +
      + +
      +
      + + 100.00% [4000/4000 00:02<00:00 Sampling 2 chains, 0 divergences] +
      + 
      Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 2 seconds.
+
      +
      +
      We recommend running at least 4 chains for robust computation of convergence diagnostics
+
      +
      +
      +
      +
      +
      +
      az.summary(idata_uneq, stat_focus="median")
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      medianmadeti_3%eti_97%mcse_medianess_medianess_tailr_hat
      Intercept5.9580.0765.7526.1580.0032601.2321480.01.0
      C(genre, levels=levels)[Action]-0.6660.098-0.953-0.3820.0032806.5451527.01.0
      sigma_Intercept0.4340.0340.3430.5430.0013218.1181644.01.0
      sigma_C(genre, levels=levels)[Action]-0.0240.051-0.1630.1100.0022837.9671694.01.0
      sigma[0]1.5080.0491.3831.6600.0023350.7671539.01.0
      ...........................
      sigma[395]1.5440.0531.4091.7220.0023218.1181644.01.0
      sigma[396]1.5440.0531.4091.7220.0023218.1181644.01.0
      sigma[397]1.5440.0531.4091.7220.0023218.1181644.01.0
      sigma[398]1.5440.0531.4091.7220.0023218.1181644.01.0
      sigma[399]1.5440.0531.4091.7220.0023218.1181644.01.0
      +

      404 rows × 8 columns

      +
      +
      +
      +
      +
      np.exp(az.summary(idata_uneq, stat_focus="median").loc["sigma_C(genre, levels=levels)[Action]","median"])
+
      +
      +
      +
      +
      0.9762857097579093
+
      +
      +
      +
      +
      +
      +

      BEST#

      +
      +
      +
      levels = ["Comedy", "Action"]
+formula_best = bmb.Formula("rating ~ 1 + C(genre,levels=levels)", "sigma ~ C(genre,levels=levels)")
+
+priors = {
+    "Intercept": bmb.Prior("Normal", mu=0, sigma=5),
+    "C(genre, levels=levels)": bmb.Prior("Normal", mu=0, sigma=1),
+    "sigma": {"C(genre, levels=levels)": bmb.Prior("Cauchy", alpha=0, beta=1)},
+    "nu": bmb.Prior("Exponential", lam=1/29),
+}
+
+# Build model
+model_best = bmb.Model(formula_best, priors=priors, family="t", data=movies)
+
+# Get model description
+print(model_best)
+# model_best.build()
+# model_best.graph()
+
      +
      +
      +
      +
             Formula: rating ~ 1 + C(genre,levels=levels)
+                sigma ~ C(genre,levels=levels)
+        Family: t
+          Link: mu = identity
+                sigma = log
+  Observations: 400
+        Priors: 
+    target = mu
+        Common-level effects
+            Intercept ~ Normal(mu: 0.0, sigma: 5.0)
+            C(genre, levels=levels) ~ Normal(mu: 0.0, sigma: 1.0)
+        
+        Auxiliary parameters
+            nu ~ Exponential(lam: 0.0345)
+    target = sigma
+        Common-level effects
+            sigma_Intercept ~ Normal(mu: 0.0, sigma: 1.0)
+            sigma_C(genre, levels=levels) ~ Cauchy(alpha: 0.0, beta: 1.0)
+
      +
      +
      +
      +
      +
      +
      idata_best = model_best.fit(draws=1000)
+
      +
      +
      +
      +
      Auto-assigning NUTS sampler...
+
      +
      +
      Initializing NUTS using jitter+adapt_diag...
+
      +
      +
      Multiprocess sampling (2 chains in 2 jobs)
+
      +
      +
      NUTS: [rating_nu, Intercept, C(genre, levels=levels), sigma_Intercept, sigma_C(genre, levels=levels)]
+
      +
      +
      + +
      +
      + + 100.00% [4000/4000 00:03<00:00 Sampling 2 chains, 6 divergences] +
      + 
      Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 4 seconds.
+
      +
      +
      We recommend running at least 4 chains for robust computation of convergence diagnostics
+
      +
      +
      +
      +
      +
      +
      az.summary(idata_best, stat_focus="median")
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      medianmadeti_3%eti_97%mcse_medianess_medianess_tailr_hat
      Intercept5.9780.0725.7746.1750.0031960.3211340.01.0
      C(genre, levels=levels)[Action]-0.6800.099-0.950-0.3810.0061847.0651631.01.0
      sigma_Intercept0.3860.0380.2670.4890.0011890.5361062.01.0
      sigma_C(genre, levels=levels)[Action]-0.0020.051-0.1370.1400.0022222.4711604.01.0
      rating_nu30.45612.9039.856109.2080.4891725.5821105.01.0
      ...........................
      sigma[395]1.4710.0551.3071.6300.0021890.5361062.01.0
      sigma[396]1.4710.0551.3071.6300.0021890.5361062.01.0
      sigma[397]1.4710.0551.3071.6300.0021890.5361062.01.0
      sigma[398]1.4710.0551.3071.6300.0021890.5361062.01.0
      sigma[399]1.4710.0551.3071.6300.0021890.5361062.01.0
      +

      405 rows × 8 columns

      +
      +
      +
      +
      +

      BEST with priors on variables instead of difference#

      +
      +
      +
      levels = ["Comedy", "Action"]
+formula_best2 = bmb.Formula("rating ~ 0 + C(genre,levels=levels)",
+                            "sigma ~ 0 + C(genre,levels=levels)")
+
+priors = {
+    "C(genre, levels=levels)": bmb.Prior("TruncatedNormal", mu=6, sigma=2, lower=1, upper=10),
+    "sigma": {"C(genre, levels=levels)": bmb.Prior("Cauchy", alpha=0, beta=1)},
+    "nu": bmb.Prior("Exponential", lam=1/29),
+}
+
+# Build model
+model_best2 = bmb.Model(formula_best2, priors=priors, family="t", data=movies)
+
+# Get model description
+print(model_best2)
+# model_best2.build()
+# model_best2.graph()
+
      +
      +
      +
      +
             Formula: rating ~ 0 + C(genre,levels=levels)
+                sigma ~ 0 + C(genre,levels=levels)
+        Family: t
+          Link: mu = identity
+                sigma = log
+  Observations: 400
+        Priors: 
+    target = mu
+        Common-level effects
+            C(genre, levels=levels) ~ TruncatedNormal(mu: 6.0, sigma: 2.0, lower: 1.0, upper: 10.0)
+        
+        Auxiliary parameters
+            nu ~ Exponential(lam: 0.0345)
+    target = sigma
+        Common-level effects
+            sigma_C(genre, levels=levels) ~ Cauchy(alpha: 0.0, beta: 1.0)
+
      +
      +
      +
      +
      +
      +
      idata_best2 = model_best2.fit(draws=1000)
+
      +
      +
      +
      +
      Auto-assigning NUTS sampler...
+
      +
      +
      Initializing NUTS using jitter+adapt_diag...
+
      +
      +
      Multiprocess sampling (2 chains in 2 jobs)
+
      +
      +
      NUTS: [rating_nu, C(genre, levels=levels), sigma_C(genre, levels=levels)]
+
      +
      +
      + +
      +
      + + 100.00% [4000/4000 00:03<00:00 Sampling 2 chains, 9 divergences] +
      + 
      Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 3 seconds.
+
      +
      +
      We recommend running at least 4 chains for robust computation of convergence diagnostics
+
      +
      +
      +
      +
      +
      +
      az.summary(idata_best2, stat_focus="median")
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      medianmadeti_3%eti_97%mcse_medianess_medianess_tailr_hat
      sigma_C(genre, levels=levels)[Comedy]0.3840.0400.2600.4940.0022159.017770.01.0
      sigma_C(genre, levels=levels)[Action]0.3850.0380.2700.4850.0012035.420757.01.0
      rating_nu30.31213.0269.449107.3290.5241823.599623.01.0
      C(genre, levels=levels)[Comedy]5.9880.0735.7966.1810.0031611.8421177.01.0
      C(genre, levels=levels)[Action]5.2970.0685.1005.4830.0031663.6701336.01.0
      ...........................
      sigma[395]1.4680.0591.2971.6390.0022159.017770.01.0
      sigma[396]1.4680.0591.2971.6390.0022159.017770.01.0
      sigma[397]1.4680.0591.2971.6390.0022159.017770.01.0
      sigma[398]1.4680.0591.2971.6390.0022159.017770.01.0
      sigma[399]1.4680.0591.2971.6390.0022159.017770.01.0
      +

      405 rows × 8 columns

      +
      +
      +
      +
      +
      np.exp(az.summary(idata_best2, stat_focus="median").loc["sigma_C(genre, levels=levels)[Action]","median"])
+
      +
      +
      +
      +
      1.4696143214411443
+
      +
      +
      +
      +
      +
      +
      +

      Example from original BEST paper#

      +

      Data taken from BESTexample-original.R in BEST.zip +via https://web.archive.org/web/20170708173718/https://www.indiana.edu/~kruschke/BEST/

      +

      Steps following Matti Vuorre’s blog post see also src notebook.

      +
      +

      Data#

      +
      +
      +
      treated = np.array([101, 100, 102, 104, 102,  97, 105, 105,  98, 101, 100, 123, 105,
+                    103, 100,  95, 102, 106, 109, 102,  82, 102, 100, 102, 102, 101,
+                    102, 102, 103, 103,  97,  97, 103, 101,  97, 104,  96, 103, 124,
+                    101, 101, 100, 101, 101, 104, 100, 101])
+controls = np.array([ 99, 101, 100, 101, 102, 100,  97, 101, 104, 101, 102, 102, 100,
+                     105,  88, 101, 100, 104, 100, 100, 100, 101, 102, 103,  97, 101,
+                     101, 100, 101,  99, 101, 100, 100, 101, 100,  99, 101, 100, 102,
+                      99, 100,  99])
+d = pd.DataFrame({
+    "group": ["treatment"]*len(treated) + ["control"]*len(controls), 
+    "iq": np.concatenate([treated, controls])
+})
+
      +
      +
      +
      +
      +
      +
      sns.histplot(data=d, x="iq", hue="group");
+
      +
      +
      +
      +../_images/bf7fd9435be6ed01b7b11fbe8242df0666f61e30a04d9f746bcbaee1f946cbc0.png +
      +
      +
      +
      +
      d.groupby("group").mean()
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + +
      iq
      group
      control100.357143
      treatment101.914894
      +
      +
      +
      +
      +

      Equal variances t-test#

      +
      +
      +
      from scipy.stats import ttest_ind
+
+res_eqvar = ttest_ind(treated, controls, equal_var=True)
+res_eqvar.statistic, res_eqvar.pvalue
+
      +
      +
      +
      +
      (1.5586953301521096, 0.12269895509665575)
+
      +
      +
      +
      +
      +
      +
      ci_eqvar = res_eqvar.confidence_interval(confidence_level=0.95)
+[ci_eqvar.low, ci_eqvar.high]
+
      +
      +
      +
      +
      ---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Cell In[28], line 1
+----> 1 ci_eqvar = res_eqvar.confidence_interval(confidence_level=0.95)
+      2 [ci_eqvar.low, ci_eqvar.high]
+
+AttributeError: 'Ttest_indResult' object has no attribute 'confidence_interval'
+
      +
      +
      +
      +
      +
      +

      Unequal variances t-test#

      +
      +
      +
      res_uneqvar = ttest_ind(treated, controls, equal_var=False)
+res_uneqvar.statistic, res_uneqvar.pvalue
+
      +
      +
      +
      +
      (1.622190457290228, 0.10975381983712831)
+
      +
      +
      +
      +
      +
      +
      ci_uneqvar = res_uneqvar.confidence_interval(confidence_level=0.95)
+[ci_uneqvar.low, ci_uneqvar.high]
+
      +
      +
      +
      +
      [-0.3611847716497789, 3.476686291406612]
+
      +
      +
      +
      +
      +
      +

      Linear model#

      +
      +
      +
      import statsmodels.formula.api as smf
+res_ols = smf.ols("iq ~ 1 + C(group)", data=d).fit()
+print(res_ols.summary())
+
      +
      +
      +
      +
                                  OLS Regression Results                            
+==============================================================================
+Dep. Variable:                     iq   R-squared:                       0.027
+Model:                            OLS   Adj. R-squared:                  0.016
+Method:                 Least Squares   F-statistic:                     2.430
+Date:                Mon, 19 Aug 2024   Prob (F-statistic):              0.123
+Time:                        22:59:33   Log-Likelihood:                -263.13
+No. Observations:                  89   AIC:                             530.3
+Df Residuals:                      87   BIC:                             535.2
+Df Model:                           1                                         
+Covariance Type:            nonrobust                                         
+=========================================================================================
+                            coef    std err          t      P>|t|      [0.025      0.975]
+-----------------------------------------------------------------------------------------
+Intercept               100.3571      0.726    138.184      0.000      98.914     101.801
+C(group)[T.treatment]     1.5578      0.999      1.559      0.123      -0.429       3.544
+==============================================================================
+Omnibus:                       46.068   Durbin-Watson:                   2.025
+Prob(Omnibus):                  0.000   Jarque-Bera (JB):              553.494
+Skew:                           1.108   Prob(JB):                    6.46e-121
+Kurtosis:                      15.014   Cond. No.                         2.69
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
      +
      +
      +
      +
      +
      +

      Alternative linear model#

      +

      Using generalized least squares to reproduce the unequal variance case.

      +
      +
      +
      n_t, var_t = len(treated), treated.var()
+n_c, var_c = len(controls), controls.var()
+sigma2s = [var_t]*n_t + [var_c]*n_c
+
+res_gls = smf.gls("iq ~ 1 + C(group)", data=d, sigma=sigma2s).fit()
+print(res_gls.summary())
+
      +
      +
      +
      +
                                  GLS Regression Results                            
+==============================================================================
+Dep. Variable:                     iq   R-squared:                       0.029
+Model:                            GLS   Adj. R-squared:                  0.018
+Method:                 Least Squares   F-statistic:                     2.629
+Date:                Mon, 19 Aug 2024   Prob (F-statistic):              0.109
+Time:                        22:59:33   Log-Likelihood:                -248.41
+No. Observations:                  89   AIC:                             500.8
+Df Residuals:                      87   BIC:                             505.8
+Df Model:                           1                                         
+Covariance Type:            nonrobust                                         
+=========================================================================================
+                            coef    std err          t      P>|t|      [0.025      0.975]
+-----------------------------------------------------------------------------------------
+Intercept               100.3571      0.388    258.627      0.000      99.586     101.128
+C(group)[T.treatment]     1.5578      0.961      1.622      0.109      -0.352       3.467
+==============================================================================
+Omnibus:                       33.582   Durbin-Watson:                   2.234
+Prob(Omnibus):                  0.000   Jarque-Bera (JB):              346.198
+Skew:                          -0.648   Prob(JB):                     6.67e-76
+Kurtosis:                      12.575   Cond. No.                         2.79
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
      +
      +
      +
      +
      +
      +
      +

      Bayesian equal variances model#

      +
      +
      +
      import bambi as bmb
+
+mod_eqvar = bmb.Model("iq ~ 1 + group", data=d)
+print(mod_eqvar)
+
      +
      +
      +
      +
             Formula: iq ~ 1 + group
+        Family: gaussian
+          Link: mu = identity
+  Observations: 89
+        Priors: 
+    target = mu
+        Common-level effects
+            Intercept ~ Normal(mu: 101.1798, sigma: 17.17)
+            group ~ Normal(mu: 0.0, sigma: 23.6275)
+        
+        Auxiliary parameters
+            sigma ~ HalfStudentT(nu: 4.0, sigma: 4.718)
+
      +
      +
      +
      +
      +
      +
      idata_eqvar = mod_eqvar.fit(draws=2000)
+
      +
      +
      +
      +
      Auto-assigning NUTS sampler...
+Initializing NUTS using jitter+adapt_diag...
+Multiprocess sampling (4 chains in 4 jobs)
+NUTS: [iq_sigma, Intercept, group]
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+
      +
      +
      + +
      +
      + + 100.00% [12000/12000 00:08<00:00 Sampling 4 chains, 0 divergences] +
      + 
      Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 20 seconds.
+
      +
      +
      +
      +
      +
      +
      import arviz as az
+
+az.summary(idata_eqvar, kind="stats")
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      meansdhdi_3%hdi_97%
      Intercept100.3580.72798.973101.722
      group[treatment]1.5541.002-0.3583.365
      iq_sigma4.7420.3604.0795.411
      +
      +
      +
      +
      +

      Bayesian unequal variances model#

      +
      +
      +
      formula = bmb.Formula("iq ~ 1 + group", "sigma ~ group")
+mod_uneqvar = bmb.Model(formula, data=d)
+print(mod_uneqvar)
+
      +
      +
      +
      +
             Formula: iq ~ 1 + group
+                sigma ~ group
+        Family: gaussian
+          Link: mu = identity
+                sigma = log
+  Observations: 89
+        Priors: 
+    target = mu
+        Common-level effects
+            Intercept ~ Normal(mu: 101.1798, sigma: 17.17)
+            group ~ Normal(mu: 0.0, sigma: 23.6275)
+    target = sigma
+        Common-level effects
+            sigma_Intercept ~ Normal(mu: 0.0, sigma: 1.0)
+            sigma_group ~ Normal(mu: 0.0, sigma: 1.0)
+
      +
      +
      +
      +
      +
      +
      idata_uneqvar = mod_uneqvar.fit(draws=2000)
+
      +
      +
      +
      +
      Auto-assigning NUTS sampler...
+Initializing NUTS using jitter+adapt_diag...
+Multiprocess sampling (4 chains in 4 jobs)
+NUTS: [Intercept, group, sigma_Intercept, sigma_group]
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+
      +
      +
      + +
      +
      + + 100.00% [12000/12000 00:10<00:00 Sampling 4 chains, 0 divergences] +
      + 
      Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 22 seconds.
+
      +
      +
      +
      +
      +
      +
      az.summary(idata_uneqvar, kind="stats")
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      meansdhdi_3%hdi_97%
      Intercept100.3570.39799.617101.105
      group[treatment]1.5530.965-0.1773.434
      sigma_Intercept0.9390.1090.7411.150
      sigma_group[treatment]0.8490.1510.5661.133
      sigma[0]6.0130.6374.8817.212
      ...............
      sigma[84]2.5740.2852.0683.121
      sigma[85]2.5740.2852.0683.121
      sigma[86]2.5740.2852.0683.121
      sigma[87]2.5740.2852.0683.121
      sigma[88]2.5740.2852.0683.121
      +

      93 rows × 4 columns

      +
      +
      +
      +
      +

      Robust Bayesian Estimation#

      +
      +
      +
      formula = bmb.Formula("iq ~ 1 + group", "sigma ~ group")
+mod_robust = bmb.Model(formula, family="t", data=d)
+print(mod_robust)
+
      +
      +
      +
      +
             Formula: iq ~ 1 + group
+                sigma ~ group
+        Family: t
+          Link: mu = identity
+                sigma = log
+  Observations: 89
+        Priors: 
+    target = mu
+        Common-level effects
+            Intercept ~ Normal(mu: 101.1798, sigma: 17.17)
+            group ~ Normal(mu: 0.0, sigma: 23.6275)
+        
+        Auxiliary parameters
+            nu ~ Gamma(alpha: 2.0, beta: 0.1)
+    target = sigma
+        Common-level effects
+            sigma_Intercept ~ Normal(mu: 0.0, sigma: 1.0)
+            sigma_group ~ Normal(mu: 0.0, sigma: 1.0)
+
      +
      +
      +
      +
      +
      +
      idata_robust = mod_robust.fit(draws=1000)
+az.summary(idata_robust, kind="stats")
+
      +
      +
      +
      +
      Auto-assigning NUTS sampler...
+Initializing NUTS using jitter+adapt_diag...
+Multiprocess sampling (4 chains in 4 jobs)
+NUTS: [iq_nu, Intercept, group, sigma_Intercept, sigma_group]
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
+
      +
      +
      + +
      +
      + + 100.00% [8000/8000 00:08<00:00 Sampling 4 chains, 0 divergences] +
      + 
      Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 20 seconds.
+
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      meansdhdi_3%hdi_97%
      Intercept100.5250.211100.142100.931
      group[treatment]1.0260.4140.2481.799
      sigma_Intercept0.0090.196-0.3640.361
      sigma_group[treatment]0.6240.2520.1561.090
      iq_nu1.8270.4871.0902.768
      ...............
      sigma[84]1.0290.2040.6771.416
      sigma[85]1.0290.2040.6771.416
      sigma[86]1.0290.2040.6771.416
      sigma[87]1.0290.2040.6771.416
      sigma[88]1.0290.2040.6771.416
      +

      94 rows × 4 columns

      +
      +
      +
      +
      + + + + +
      + + + + + + +
      + +
      +
      +
      + +
      + + + +
      + +
      +
      + Contents +
      +
      + +
      + + +
      +
      + +
      + +
      + +

      +By Ivan Savov +

      + +
      + +
      + + +

      + + © Copyright 2023. +
      + +

      + +
      + +
      + +
      + +
      + +
      + +
      +
      + + +
      +
      +
      + + + + + +
      +
      + + \ No newline at end of file diff --git a/notebooks/54_Bayesian_linear_models.html b/notebooks/54_Bayesian_linear_models.html new file mode 100644 index 00000000..c9463985 --- /dev/null +++ b/notebooks/54_Bayesian_linear_models.html @@ -0,0 +1,889 @@ + + + + + + + + + + + + Section 5.4 — Bayesian linear models — No BS Stats Notebooks + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + + + + + + + + + + + +
      +
      +
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      + + + Ctrl+K +
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      + +
      + +
      +
      + + + +
      +

      Section 5.4 — Bayesian linear models

      + +
      + +
      +
      + + + + +
      + +
      +

      Section 5.4 — Bayesian linear models#

      +

      This notebook contains the code examples from Section 5.4 Bayesian linear models from the No Bullshit Guide to Statistics.

      +

      See also examples in:

      +
        +

      • BambiRegression.ipynb.

        • +

      • chp_03.ipynb

        • +

      • ESCS_multiple_regression.ipynb

        • +
      +
      +

      Notebook setup#

      +
      +
      +
      # load Python modules
+import os
+import numpy as np
+import pandas as pd
+import seaborn as sns
+import matplotlib.pyplot as plt
+
      +
      +
      +
      +
      +
      +
      # Figures setup
+plt.clf()  # needed otherwise `sns.set_theme` doesn"t work
+from plot_helpers import RCPARAMS
+RCPARAMS.update({"figure.figsize": (5, 3)})   # good for screen
+# RCPARAMS.update({"figure.figsize": (5, 1.6)})  # good for print
+sns.set_theme(
+    context="paper",
+    style="whitegrid",
+    palette="colorblind",
+    rc=RCPARAMS,
+)
+
+# High-resolution please
+%config InlineBackend.figure_format = "retina"
+
+# Where to store figures
+DESTDIR = "figures/bayesian/lms"
+
      +
      +
      +
      +
      <Figure size 640x480 with 0 Axes>
+
      +
      +
      +
      +
      +
      +
      # set random seed for repeatability
+np.random.seed(42)
+
      +
      +
      +
      +
      +
      +

      Simple linear regression using PyMC#

      +
      +
      +
      import pymc as pm
+import numpy as np
+import arviz as az
+
+# Simulated data
+np.random.seed(42)
+x = np.random.normal(0, 1, 100)
+y = 3 + 2 * x + np.random.normal(0, 1, 100)
+
+# Bayesian Linear Regression Model
+with pm.Model() as model:
+    # Priors
+    beta0 = pm.Normal("beta0", mu=0, sigma=10)
+    beta1 = pm.Normal("beta1", mu=0, sigma=10)
+    sigma = pm.HalfNormal("sigma", sigma=1)
+    
+    # Likelihood
+    mu = beta0 + beta1 * x
+    y_obs = pm.Normal("y_obs", mu=mu, sigma=sigma, observed=y)
+    
+    # Sampling
+    trace = pm.sample(2000, return_inferencedata=True)
+
      +
      +
      +
      +
      Auto-assigning NUTS sampler...
+
      +
      +
      Initializing NUTS using jitter+adapt_diag...
+
      +
      +
      Multiprocess sampling (2 chains in 2 jobs)
+
      +
      +
      NUTS: [beta0, beta1, sigma]
+
      +
      +
      + +
      +
      + + 100.00% [6000/6000 00:02<00:00 Sampling 2 chains, 0 divergences] +
      + 
      Sampling 2 chains for 1_000 tune and 2_000 draw iterations (2_000 + 4_000 draws total) took 3 seconds.
+
      +
      +
      We recommend running at least 4 chains for robust computation of convergence diagnostics
+
      +
      +
      +
      +
      +

      Summary using mean#

      +
      +
      +
      # Posterior Summary
+summary = az.summary(trace, kind="stats")
+summary
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      meansdhdi_3%hdi_97%
      beta03.0090.0982.8243.188
      beta11.8560.1081.6672.071
      sigma0.9590.0700.8391.102
      +
      +
      +
      +
      +

      Summary using median as focus statistic#

      +

      ETI = Equal-Tailed Interval

      +
      +
      +
      az.summary(trace, stat_focus="median", kind="stats")
+
      +
      +
      +
      +
      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      medianmadeti_3%eti_97%
      beta03.0100.0652.8273.192
      beta11.8560.0731.6512.059
      sigma0.9540.0450.8401.104
      +
      +
      +
      +
      +
      # Plotting posterior
+az.plot_posterior(trace, point_estimate="mean", round_to=3);
+
      +
      +
      +
      +../_images/80c5529eb521d25833f837d0e232c29b93f5154f6b867f07b377170b6e64debf.png +
      +
      +
      +
      +
      + + + + +
      + + + + + + +
      + +
      +
      +
      + +
      + + + +
      + +
      +
      + Contents +
      +
      + +
      + + +
      +
      + +
      + +
      + +

      +By Ivan Savov +

      + +
      + +
      + + +

      + + © Copyright 2023. +
      + +

      + +
      + +
      + +
      + +
      + +
      + +
      +
      + + +
      +
      +
      + + + + + +
      +
      + + \ No newline at end of file diff --git a/notebooks/55_hierarchical_models.html b/notebooks/55_hierarchical_models.html new file mode 100644 index 00000000..d9fec8b2 --- /dev/null +++ b/notebooks/55_hierarchical_models.html @@ -0,0 +1,668 @@ + + + + + + + + + + + + Section 5.5 — Hierarchical models — No BS Stats Notebooks + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + + + + + + + + + + + +
      +
      +
      +
      + + + Ctrl+K +
      +
      + + + +
      +
      + +
      + + + +
      + + + + +
      + +
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      + + + +
      +
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      + + +
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      + + + + + + +
      + + +
      + + + + + + + + + + + + + +
      + +
      + +
      +
      + + + +
      +

      Section 5.5 — Hierarchical models

      + +
      +
      + +
      +

      Contents

      +
      + +
      +
      +
      + + + + +
      + +
      +

      Section 5.5 — Hierarchical models#

      +

      This notebook contains the code examples from Section 5.5 Hierarchical models from the No Bullshit Guide to Statistics.

      +
      +

      Notebook setup#

      +
      +
      +
      # load Python modules
+import os
+import numpy as np
+import pandas as pd
+import seaborn as sns
+import matplotlib.pyplot as plt
+
      +
      +
      +
      +
      +
      +
      # Figures setup
+plt.clf()  # needed otherwise `sns.set_theme` doesn"t work
+from plot_helpers import RCPARAMS
+RCPARAMS.update({"figure.figsize": (5, 3)})   # good for screen
+# RCPARAMS.update({"figure.figsize": (5, 1.6)})  # good for print
+sns.set_theme(
+    context="paper",
+    style="whitegrid",
+    palette="colorblind",
+    rc=RCPARAMS,
+)
+
+# High-resolution please
+%config InlineBackend.figure_format = "retina"
+
+# Where to store figures
+DESTDIR = "figures/bayesian/hierarchical"
+
      +
      +
      +
      +
      <Figure size 640x480 with 0 Axes>
+
      +
      +
      +
      +
      +
      +
      # set random seed for repeatability
+np.random.seed(42)
+#######################################################
+
      +
      +
      +
      +
      +
      + + + + +
      + + + + + + +
      + +
      +
      +
      + +
      + + + +
      + +
      +
      + Contents +
      +
      + +
      + + +
      +
      + +
      + +
      + +

      +By Ivan Savov +

      + +
      + +
      + + +

      + + © Copyright 2023. +
      + +

      + +
      + +
      + +
      + +
      + +
      + +
      +
      + + +
      +
      +
      + + + + + +
      +
      + + \ No newline at end of file diff --git a/objects.inv b/objects.inv index 9bd66f2f..f3866d24 100644 Binary files a/objects.inv and b/objects.inv differ diff --git a/reports/notebooks/46_generalized_linear_models.err.log b/reports/notebooks/46_generalized_linear_models.err.log index 71734a52..ae2e9291 100644 --- a/reports/notebooks/46_generalized_linear_models.err.log +++ b/reports/notebooks/46_generalized_linear_models.err.log @@ -15,297 +15,14 @@ Traceback (most recent call last): raise CellExecutionError.from_cell_and_msg(cell, exec_reply_content) nbclient.exceptions.CellExecutionError: An error occurred while executing the following cell: ------------------ -# FIGURES ONLY -fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(6, 2)) - -# plot the expit function, a.k.a. the logistic function -xs = np.linspace(-6, 6, 500) -sns.lineplot(x=xs, y=expit(xs), ax=ax1, label="$\\text{expit}(x)$") -ax1.set_xlabel("$x$") -ax1.set_ylabel("$p$") - -# plot the logit function -ps = np.linspace(0, 1, 600) -sns.lineplot(x=ps, y=logit(ps), ax=ax2, label="$\\text{logit}(p)$", color="C1") -ax2.set_xlabel("$p$") -ax2.set_ylabel("$x$") - - -filename = os.path.join(DESTDIR, "logistic_and_logit_functions.pdf") -savefigure(fig, filename, tight_layout_kwargs=dict(w_pad=3)) +import marginaleffects as me ------------------ ------ stdout ----- -Error in callback (for post_execute): ------------------- --------------------------------------------------------------------------- -ValueError Traceback (most recent call last) -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/IPython/core/formatters.py:340, in BaseFormatter.__call__(self, obj) - 338 pass - 339 else: ---> 340 return printer(obj) - 341 # Finally look for special method names - 342 method = get_real_method(obj, self.print_method) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:169, in retina_figure(fig, base64, **kwargs) - 160 def retina_figure(fig, base64=False, **kwargs): - 161  """format a figure as a pixel-doubled (retina) PNG - 162 - 163  If `base64` is True, return base64-encoded str instead of raw bytes - (...) - 167  base64 argument - 168  """ ---> 169 pngdata = print_figure(fig, fmt="retina", base64=False, **kwargs) - 170 # Make sure that retina_figure acts just like print_figure and returns - 171 # None when the figure is empty. - 172 if pngdata is None: - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/IPython/core/pylabtools.py:152, in print_figure(fig, fmt, bbox_inches, base64, **kwargs) - 149 from matplotlib.backend_bases import FigureCanvasBase - 150 FigureCanvasBase(fig) ---> 152 fig.canvas.print_figure(bytes_io, **kw) - 153 data = bytes_io.getvalue() - 154 if fmt == 'svg': - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/backend_bases.py:2342, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs) - 2336 renderer = _get_renderer( - 2337 self.figure, - 2338 functools.partial( - 2339 print_method, orientation=orientation) - 2340 ) - 2341 with getattr(renderer, "_draw_disabled", nullcontext)(): --> 2342 self.figure.draw(renderer) - 2344 if bbox_inches: - 2345 if bbox_inches == "tight": - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:95, in _finalize_rasterization..draw_wrapper(artist, renderer, *args, **kwargs) - 93 @wraps(draw) - 94 def draw_wrapper(artist, renderer, *args, **kwargs): ----> 95 result = draw(artist, renderer, *args, **kwargs) - 96 if renderer._rasterizing: - 97 renderer.stop_rasterizing() - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:72, in allow_rasterization..draw_wrapper(artist, renderer) - 69 if artist.get_agg_filter() is not None: - 70 renderer.start_filter() ----> 72 return draw(artist, renderer) - 73 finally: - 74 if artist.get_agg_filter() is not None: - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/figure.py:3175, in Figure.draw(self, renderer) - 3172 # ValueError can occur when resizing a window. - 3174 self.patch.draw(renderer) --> 3175 mimage._draw_list_compositing_images( - 3176  renderer, self, artists, self.suppressComposite) - 3178 for sfig in self.subfigs: - 3179 sfig.draw(renderer) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/image.py:131, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite) - 129 if not_composite or not has_images: - 130 for a in artists: ---> 131 a.draw(renderer) - 132 else: - 133 # Composite any adjacent images together - 134 image_group = [] - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:72, in allow_rasterization..draw_wrapper(artist, renderer) - 69 if artist.get_agg_filter() is not None: - 70 renderer.start_filter() ----> 72 return draw(artist, renderer) - 73 finally: - 74 if artist.get_agg_filter() is not None: - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/axes/_base.py:3064, in _AxesBase.draw(self, renderer) - 3061 if artists_rasterized: - 3062 _draw_rasterized(self.figure, artists_rasterized, renderer) --> 3064 mimage._draw_list_compositing_images( - 3065  renderer, self, artists, self.figure.suppressComposite) - 3067 renderer.close_group('axes') - 3068 self.stale = False - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/image.py:131, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite) - 129 if not_composite or not has_images: - 130 for a in artists: ---> 131 a.draw(renderer) - 132 else: - 133 # Composite any adjacent images together - 134 image_group = [] - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/artist.py:72, in allow_rasterization..draw_wrapper(artist, renderer) - 69 if artist.get_agg_filter() is not None: - 70 renderer.start_filter() ----> 72 return draw(artist, renderer) - 73 finally: - 74 if artist.get_agg_filter() is not None: - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/legend.py:726, in Legend.draw(self, renderer) - 722 self._legend_box.set_width(self.get_bbox_to_anchor().width - pad) - 724 # update the location and size of the legend. This needs to - 725 # be done in any case to clip the figure right. ---> 726 bbox = self._legend_box.get_window_extent(renderer) - 727 self.legendPatch.set_bounds(bbox.bounds) - 728 self.legendPatch.set_mutation_scale(fontsize) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:400, in OffsetBox.get_window_extent(self, renderer) - 398 if renderer is None: - 399 renderer = self.figure._get_renderer() ---> 400 bbox = self.get_bbox(renderer) - 401 try: # Some subclasses redefine get_offset to take no args. - 402 px, py = self.get_offset(bbox, renderer) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer) - 365 def get_bbox(self, renderer): - 366  """Return the bbox of the offsetbox, ignoring parent offsets.""" ---> 367 bbox, offsets = self._get_bbox_and_child_offsets(renderer) - 368 return bbox - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in VPacker._get_bbox_and_child_offsets(self, renderer) - 482 if isinstance(c, PackerBase) and c.mode == "expand": - 483 c.set_width(self.width) ---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()] - 486 (x0, x1), xoffsets = _get_aligned_offsets( - 487 [bbox.intervalx for bbox in bboxes], self.width, self.align) - 488 height, yoffsets = _get_packed_offsets( - 489 [bbox.height for bbox in bboxes], self.height, sep, self.mode) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in (.0) - 482 if isinstance(c, PackerBase) and c.mode == "expand": - 483 c.set_width(self.width) ---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()] - 486 (x0, x1), xoffsets = _get_aligned_offsets( - 487 [bbox.intervalx for bbox in bboxes], self.width, self.align) - 488 height, yoffsets = _get_packed_offsets( - 489 [bbox.height for bbox in bboxes], self.height, sep, self.mode) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer) - 365 def get_bbox(self, renderer): - 366  """Return the bbox of the offsetbox, ignoring parent offsets.""" ---> 367 bbox, offsets = self._get_bbox_and_child_offsets(renderer) - 368 return bbox - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in HPacker._get_bbox_and_child_offsets(self, renderer) - 509 pad = self.pad * dpicor - 510 sep = self.sep * dpicor ---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()] - 513 if not bboxes: - 514 return Bbox.from_bounds(0, 0, 0, 0).padded(pad), [] - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in (.0) - 509 pad = self.pad * dpicor - 510 sep = self.sep * dpicor ---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()] - 513 if not bboxes: - 514 return Bbox.from_bounds(0, 0, 0, 0).padded(pad), [] - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer) - 365 def get_bbox(self, renderer): - 366  """Return the bbox of the offsetbox, ignoring parent offsets.""" ---> 367 bbox, offsets = self._get_bbox_and_child_offsets(renderer) - 368 return bbox - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in VPacker._get_bbox_and_child_offsets(self, renderer) - 482 if isinstance(c, PackerBase) and c.mode == "expand": - 483 c.set_width(self.width) ---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()] - 486 (x0, x1), xoffsets = _get_aligned_offsets( - 487 [bbox.intervalx for bbox in bboxes], self.width, self.align) - 488 height, yoffsets = _get_packed_offsets( - 489 [bbox.height for bbox in bboxes], self.height, sep, self.mode) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:485, in (.0) - 482 if isinstance(c, PackerBase) and c.mode == "expand": - 483 c.set_width(self.width) ---> 485 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()] - 486 (x0, x1), xoffsets = _get_aligned_offsets( - 487 [bbox.intervalx for bbox in bboxes], self.width, self.align) - 488 height, yoffsets = _get_packed_offsets( - 489 [bbox.height for bbox in bboxes], self.height, sep, self.mode) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:367, in OffsetBox.get_bbox(self, renderer) - 365 def get_bbox(self, renderer): - 366  """Return the bbox of the offsetbox, ignoring parent offsets.""" ---> 367 bbox, offsets = self._get_bbox_and_child_offsets(renderer) - 368 return bbox - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in HPacker._get_bbox_and_child_offsets(self, renderer) - 509 pad = self.pad * dpicor - 510 sep = self.sep * dpicor ---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()] - 513 if not bboxes: - 514 return Bbox.from_bounds(0, 0, 0, 0).padded(pad), [] - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:512, in (.0) - 509 pad = self.pad * dpicor - 510 sep = self.sep * dpicor ---> 512 bboxes = [c.get_bbox(renderer) for c in self.get_visible_children()] - 513 if not bboxes: - 514 return Bbox.from_bounds(0, 0, 0, 0).padded(pad), [] - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/offsetbox.py:801, in TextArea.get_bbox(self, renderer) - 796 def get_bbox(self, renderer): - 797 _, h_, d_ = renderer.get_text_width_height_descent( - 798 "lp", self._text._fontproperties, - 799 ismath="TeX" if self._text.get_usetex() else False) ---> 801 bbox, info, yd = self._text._get_layout(renderer) - 802 w, h = bbox.size - 804 self._baseline_transform.clear() - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:386, in Text._get_layout(self, renderer) - 384 clean_line, ismath = self._preprocess_math(line) - 385 if clean_line: ---> 386 w, h, d = _get_text_metrics_with_cache( - 387  renderer, clean_line, self._fontproperties, - 388  ismath=ismath, dpi=self.figure.dpi) - 389 else: - 390 w = h = d = 0 - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:97, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi) - 94 """Call ``renderer.get_text_width_height_descent``, caching the results.""" - 95 # Cached based on a copy of fontprop so that later in-place mutations of - 96 # the passed-in argument do not mess up the cache. ----> 97 return _get_text_metrics_with_cache_impl( - 98  weakref.ref(renderer), text, fontprop.copy(), ismath, dpi) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/text.py:105, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi) - 101 @functools.lru_cache(4096) - 102 def _get_text_metrics_with_cache_impl( - 103 renderer_ref, text, fontprop, ismath, dpi): - 104 # dpi is unused, but participates in cache invalidation (via the renderer). ---> 105 return renderer_ref().get_text_width_height_descent(text, fontprop, ismath) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/backends/backend_agg.py:230, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath) - 226 return super().get_text_width_height_descent(s, prop, ismath) - 228 if ismath: - 229 ox, oy, width, height, descent, font_image = \ ---> 230 self.mathtext_parser.parse(s, self.dpi, prop) - 231 return width, height, descent - 233 font = self._prepare_font(prop) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/mathtext.py:226, in MathTextParser.parse(self, s, dpi, prop) - 222 # lru_cache can't decorate parse() directly because prop - 223 # is mutable; key the cache using an internal copy (see - 224 # text._get_text_metrics_with_cache for a similar case). - 225 prop = prop.copy() if prop is not None else None ---> 226 return self._parse_cached(s, dpi, prop) - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/mathtext.py:247, in MathTextParser._parse_cached(self, s, dpi, prop) - 244 if self._parser is None: # Cache the parser globally. - 245 self.__class__._parser = _mathtext.Parser() ---> 247 box = self._parser.parse(s, fontset, fontsize, dpi) - 248 output = _mathtext.ship(box) - 249 if self._output_type == "vector": - -File /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/matplotlib/_mathtext.py:1971, in Parser.parse(self, s, fonts_object, fontsize, dpi) - 1968 result = self._expression.parseString(s) - 1969 except ParseBaseException as err: - 1970 # explain becomes a plain method on pyparsing 3 (err.explain(0)). --> 1971 raise ValueError("\n" + ParseException.explain(err, 0)) from None - 1972 self._state_stack = None - 1973 self._in_subscript_or_superscript = False +ModuleNotFoundError Traceback (most recent call last) +Cell In[50], line 1 +----> 1 import marginaleffects as me -ValueError: -\text{expit}(x) -^ -ParseFatalException: Unknown symbol: \text, found '\' (at char 0), (line:1, col:1) +ModuleNotFoundError: No module named 'marginaleffects' diff --git a/reports/notebooks/50_extra_bayesian_stuff.err.log b/reports/notebooks/50_extra_bayesian_stuff.err.log new file mode 100644 index 00000000..b512a518 --- /dev/null +++ b/reports/notebooks/50_extra_bayesian_stuff.err.log @@ -0,0 +1,37 @@ +Traceback (most recent call last): + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 778, in _async_poll_for_reply + msg = await ensure_async(self.kc.shell_channel.get_msg(timeout=new_timeout)) + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 198, in ensure_async + result = await obj + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_client/channels.py", line 313, in get_msg + raise Empty +_queue.Empty + +During handling of the above exception, another exception occurred: + +Traceback (most recent call last): + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_cache/executors/utils.py", line 58, in single_nb_execution + executenb( + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 1305, in execute + return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute() + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped + return loop.run_until_complete(inner) + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/asyncio/base_events.py", line 616, in run_until_complete + return future.result() + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 705, in async_execute + await self.async_execute_cell( + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 1001, in async_execute_cell + exec_reply = await self.task_poll_for_reply + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 802, in _async_poll_for_reply + error_on_timeout_execute_reply = await self._async_handle_timeout(timeout, cell) + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 852, in _async_handle_timeout + raise CellTimeoutError.error_from_timeout_and_cell( +nbclient.exceptions.CellTimeoutError: A cell timed out while it was being executed, after 30 seconds. +The message was: Cell execution timed out. +Here is a preview of the cell contents: +------------------- +['import pymc as pm', 'import numpy as np', 'import arviz as az', '', '# Simulated data'] +... +[' mu = beta0 + beta1 * x', ' y_obs = pm.Normal("y_obs", mu=mu, sigma=sigma, observed=y)', ' ', ' # Sampling', ' trace = pm.sample(2000, return_inferencedata=True)'] +------------------- + diff --git a/reports/notebooks/53_difference_between_means.err.log b/reports/notebooks/53_difference_between_means.err.log new file mode 100644 index 00000000..91e9b0f1 --- /dev/null +++ b/reports/notebooks/53_difference_between_means.err.log @@ -0,0 +1,30 @@ +Traceback (most recent call last): + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_cache/executors/utils.py", line 58, in single_nb_execution + executenb( + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 1305, in execute + return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute() + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped + return loop.run_until_complete(inner) + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/asyncio/base_events.py", line 616, in run_until_complete + return future.result() + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 705, in async_execute + await self.async_execute_cell( + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 1058, in async_execute_cell + await self._check_raise_for_error(cell, cell_index, exec_reply) + File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 914, in _check_raise_for_error + raise CellExecutionError.from_cell_and_msg(cell, exec_reply_content) +nbclient.exceptions.CellExecutionError: An error occurred while executing the following cell: +------------------ +ci_eqvar = res_eqvar.confidence_interval(confidence_level=0.95) +[ci_eqvar.low, ci_eqvar.high] +------------------ + + +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In[28], line 1 +----> 1 ci_eqvar = res_eqvar.confidence_interval(confidence_level=0.95) + 2 [ci_eqvar.low, ci_eqvar.high] + +AttributeError: 'Ttest_indResult' object has no attribute 'confidence_interval' + diff --git a/searchindex.js b/searchindex.js index c9c1043f..6c299c2b 100644 --- a/searchindex.js +++ b/searchindex.js @@ -1 +1 @@ -Search.setIndex({"docnames": ["DESIGN", "blogposts/README", "blogposts/cut_material", "blogposts/python_for_stats", "blogposts/python_for_stats2", "casestudies/README", "datasets/README", "datasets/exercises/README", "datasets/index", "examples/ANOVA", "examples/Mann-Whitney_U-test", "examples/README", "examples/one_sample_t-test", 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"tutorials/pandas_tutorial.ipynb", "tutorials/python_tutorial.ipynb", "tutorials/seaborn_tutorial.ipynb", "tutorials/src/cut_material.md", "tutorials/src/pycut_material.ipynb", "tutorials/src/python_tutorial_src.ipynb"], "titles": ["Software design", "Blog posts", "CUT MATERIAL", "Using Python for learning statistics Part 1", "Using Python for learning statistics Part 2", "Statistical analysis case studies", "Datasets", "Datasets for exercises", "Datasets", "Analysis of variance (ANOVA)", "Mann-Whitney U-test", "Statistical analysis examples", "One-sample t-test for the mean", "One-sample z-test for the mean", "Statistical design examples", "Two-way ANOVA", "Two-sample equivalence test", "Welch\u2019s two-sample \\(t\\)-test", "Datasets", "Datasets for exercises", "Datasets", "Practical data exercises", "Descriptive statistics exercises", "Exercises for Section 2.1 Discrete random variables", "Exercises for Section 3.1 Estimates and estimators", "Exercises for Section 3.2 Confidence intervals", "Exercises for Section 3.3 Introduction to hypothesis testing", "Exercises for Section 3.5 Two-sample tests", "Solutions to Chapter 1 (DATA) problems", "Datasets", "Datasets for exercises", "Datasets", "Exercises for Section 3.1 Estimates and estimators", "Exercises for Section 3.2 Confidence intervals", "No Bullshit Stats Notebooks", "Chapter 1 \u2014 Data", "Section 1.1 \u2014 Introduction to data", "Section 1.2 \u2014 Data in practice", "Section 1.3 \u2014 Descriptive statistics", "Chapter 2 \u2014 Probability theory", "Section 2.1 \u2014 Discrete random variables", "Section 2.2 \u2014 Multiple random variables", "Section 2.3 \u2014 Inventory of discrete distributions", "Section 2.4 \u2014 Calculus prerequisites", "Section 2.5 \u2014 Continuous random variables", "Section 2.6 \u2014 Inventory of continuous distributions", "Section 2.7 \u2014 Random variable generation", "Section 2.8 \u2014 Probability models for random samples", "Chapter 3 \u2014 Inferential statistics", "Section 3.1 \u2014 Estimators", "Section 3.2 \u2014 Confidence intervals", "Section 3.3 \u2014 Introduction to hypothesis testing", "Section 3.4 \u2014 Hypothesis testing using analytical approximations", "Section 3.5 \u2014 Two-sample hypothesis tests", "Section 3.6 \u2014 Statistical design and error analysis", "Section 3.7 \u2014 Inventory of statistical tests", "Chapter 4 \u2014 Linear models", "CH4 extra stuff", "Section 4.1 \u2014 Simple linear regression", "Section 4.2 \u2014 Multiple linear regression", "Section 4.3 \u2014 Interpreting linear models", "Section 4.4 \u2014 Regression with categorical predictors", "Section 4.5 \u2014 Model selection for causal inference", "Section 4.6 \u2014 Generalized linear models", "Chapter 5 \u2014 Bayesian statistics", "Sampling distribution of the mean details", "Estimators for categorical variables", "OLD Section 3.4 \u2014 Analytical approximation methods", "Notebooks", "<no title>", "CUT MATERIAL", "Notebooks", "Comparing one group to a 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70, 79, 81, 83, 87, 91], "0505": 4, "seed": [4, 9, 12, 13, 16, 17, 25, 26, 32, 33, 36, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 65, 66, 67, 70, 72, 75, 76, 80, 81], "ci": [4, 37, 50, 51, 52, 53, 57, 58, 63, 65, 66, 67, 70, 75, 76, 81, 82], "confidence_interv": [4, 50, 52, 61, 66, 70, 81], "confidence_level": [4, 50, 52, 61, 70, 81], "low": [4, 16, 43, 49, 50, 51, 52, 57, 61, 62, 63, 70, 81, 87, 91], "9049": 4, "clever": [4, 83], "techniqu": [4, 11, 49, 68, 70, 71, 78, 80, 83, 86, 88], "5000": [4, 32, 49, 50, 57, 70, 81, 89], "replac": [4, 12, 13, 40, 49, 53, 54, 55, 57, 60, 63, 68, 70, 71, 77, 79, 81, 86, 87, 90, 91], "data_url": 4, "panda": [4, 6, 8, 9, 10, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 38, 40, 42, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 74, 75, 76, 80, 81, 82, 84, 87, 88, 90, 91], "xbars_boot": [4, 50], "true": [4, 9, 11, 15, 17, 22, 27, 37, 38, 43, 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62, 63, 66, 67, 70, 74, 77, 79, 81, 86, 87, 90, 91], "xbar_boot": 4, "bootstrap_dist_mean_epricesw": 4, "citi": [4, 25, 33, 37, 49, 86], "term": [4, 15, 24, 25, 32, 33, 37, 39, 40, 49, 50, 52, 54, 61, 80, 81, 86, 87, 90, 91], "averag": [4, 40, 44, 49, 50, 62, 81, 86, 90], "xsampl": [4, 17, 24, 25, 26, 27, 32, 33, 49, 50, 53, 66, 67, 70], "ysampl": [4, 17, 24, 25, 26, 27, 32, 33, 49, 50, 53, 66, 67, 70], "dprice": [4, 53, 70], "hypothesi": [4, 12, 13, 16, 17, 48, 49, 55, 67, 86], "42": [4, 9, 12, 13, 16, 17, 23, 25, 26, 32, 33, 41, 42, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 70, 72, 75, 76, 80, 81, 87, 89, 90, 91], "pdhat": [4, 53], "allpric": 4, "pallpric": 4, "psamplew": 4, "psample": 4, "0002": [4, 53, 70], "blue": [4, 24, 26, 32, 38, 49, 52, 53, 54, 55, 57, 60, 65, 66, 67, 70, 72, 75, 76, 79, 80, 81, 82], "bin": [4, 22, 32, 38, 49, 50, 51, 53, 63, 65, 70, 72, 81], "100": [4, 6, 8, 9, 12, 13, 16, 17, 18, 20, 24, 29, 31, 32, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 54, 57, 58, 60, 62, 63, 65, 72, 76, 80, 81, 82, 83, 86, 87, 89, 90, 91], "axvlin": [4, 49, 51, 53, 65, 70, 72, 79, 81], "f_": [4, 32, 40, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 65, 66, 67, 68, 70, 71, 81], "widehat": [4, 17, 49, 50, 51, 52, 53, 58, 60, 62, 66, 70], "_0": [4, 51, 52, 53, 70], "pvalue_viz_permutation_test_epric": 4, "estfunc": [4, 24, 26, 32, 33, 49, 50, 51, 65, 70, 75], "bestim": [4, 49], "zbars_boot": 4, "permutation_test_dmean": [4, 27, 53], "obsdhat": [4, 16, 17, 53, 70], "get": [4, 9, 15, 22, 38, 39, 40, 44, 45, 47, 49, 51, 53, 57, 60, 62, 63, 65, 68, 71, 72, 75, 78, 79, 80, 81, 82, 83, 88, 89], "dist": [4, 46, 49, 50, 53, 65, 66, 70, 75], "101": [4, 12, 13, 16, 21, 36, 40, 53, 54, 57, 60, 63, 81, 83], "student": [4, 5, 12, 16, 17, 22, 24, 27, 28, 32, 50, 53, 57, 61, 65, 70, 74, 83, 87, 90, 91], "contact": 4, "wa": [4, 6, 8, 16, 18, 20, 25, 29, 31, 33, 37, 42, 51, 60, 62, 81, 82, 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81, 86, 87, 89, 90, 91], "400": [4, 23, 60, 61, 63, 70, 80], "With": [4, 34, 62], "littl": [4, 40, 44, 46, 50, 59, 81, 82, 86, 87, 89, 90, 91], "bit": [4, 39, 40, 50, 65, 68, 71, 85, 86, 87, 89, 90, 91], "knowledg": [4, 37, 40, 50, 65, 70, 81, 86], "allen": [4, 51], "downei": [4, 51], "hacker": [4, 51], "jake": [4, 51], "vanderpla": [4, 51], "realist": [5, 65, 70, 81], "analys": [5, 79, 86], "collect": [5, 6, 8, 18, 20, 26, 29, 31, 37, 49, 57, 63, 70, 78, 79, 80, 82, 89, 90], "clean": [5, 6, 8, 18, 20, 29, 31, 68, 71, 81, 87, 91], "hypothei": [5, 82], "fomul": 5, "repot": 5, "purpos": [5, 11, 39, 68, 70, 71, 80, 81, 86, 87, 90, 91], "illustr": [5, 11, 34, 40, 50, 53, 69, 78, 79, 81, 83, 86, 87, 90, 91], "numer": [5, 6, 8, 9, 10, 12, 13, 16, 17, 18, 20, 29, 31, 37, 40, 41, 49, 51, 57, 61, 68, 71, 79, 81, 83, 86, 90], "non": [5, 16, 37, 38, 40, 52, 61, 62, 70, 80, 82, 86, 87, 89, 90, 91], "real": [5, 11, 34, 40, 44, 49, 53, 62, 70, 80, 81, 86, 87, 89, 90, 91], "world": [5, 11, 34, 40, 44, 49, 62, 80, 86, 87, 89, 90, 91], "visitor": [5, 6, 8, 18, 20, 29, 31, 66], "electr": 5, "player": [5, 21, 70, 90], "background": [5, 6, 8, 18, 20, 22, 28, 29, 31, 37, 58, 86, 87, 90, 91], "stori": [5, 37, 86, 87, 90, 91], "question": [5, 9, 37, 44, 51, 61, 63, 70, 79, 83, 86, 87, 89, 91], "place": [5, 34, 60, 63, 81, 86, 87, 89, 90, 91], "produc": [5, 12, 13, 39, 40, 70, 78, 79, 81, 87, 88, 89, 90, 91], "report": [5, 40, 46, 50, 51, 53, 60, 63, 81, 82, 86], "archiv": [5, 37], "folder": [6, 8, 18, 20, 29, 31, 37, 39, 57, 68, 71, 86, 87, 91], "store": [6, 8, 17, 18, 20, 24, 29, 31, 32, 37, 40, 42, 43, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 70, 72, 73, 79, 86, 87, 90, 91], "inform": [6, 8, 18, 20, 29, 31, 37, 40, 44, 63, 70, 81, 86, 87, 90, 91], "extens": [6, 8, 18, 20, 29, 31, 37, 86, 87, 90, 91], "md": [6, 8, 18, 20, 29, 31, 68, 71], "game": [6, 8, 18, 20, 29, 31, 37, 86], "players_ful": [6, 8, 18, 20, 29, 31, 57], "confound": [6, 8, 18, 20, 29, 31, 56, 70, 80], "jobstatu": [6, 8, 18, 20, 29, 31], "appendix": [6, 8, 18, 20, 29, 31, 37], "miss": [6, 8, 18, 20, 29, 31, 79, 82, 83, 87, 91], "These": [6, 8, 18, 20, 29, 31, 34, 50, 57, 68, 71, 83, 86, 87, 91], "locat": [6, 8, 18, 20, 24, 25, 29, 31, 32, 33, 34, 44, 45, 52, 60, 63, 70, 86, 87, 90, 91], "charg": [6, 8, 18, 20, 29, 31, 37, 49, 86], "station": [6, 8, 18, 20, 29, 31, 37, 49, 86], "descript": [6, 8, 18, 20, 29, 31, 35, 37, 43, 49, 50, 51, 53, 60, 81, 83, 86, 87, 90, 91], "consist": [6, 8, 10, 17, 18, 20, 29, 31, 37, 38, 40, 47, 49, 63, 83, 86, 87, 89, 91], "activ": [6, 8, 18, 20, 29, 31, 87, 91], "onlin": [6, 8, 18, 20, 29, 31, 79, 86, 87, 90, 91], "platform": [6, 8, 18, 20, 29, 31, 86, 87, 91], "scienc": [6, 8, 18, 20, 22, 28, 29, 31, 37, 38, 58, 60, 70, 78, 81, 86], "teacher": [6, 8, 18, 20, 29, 31, 37, 51, 86, 87, 91], "compar": [6, 8, 10, 12, 13, 17, 18, 20, 24, 25, 29, 31, 32, 33, 37, 47, 49, 51, 52, 55, 57, 60, 66, 70, 78, 80, 86, 87, 90, 91], "effect": [6, 8, 11, 14, 18, 20, 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      Visualizations
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      -../_images/f4dd33cf27a95e819664fe10fb012825babb0f0fff0019d4ea1564cfd13b583c.png +../_images/a8664b40fd1f1c5d76f5a759a3956d463793dc66e0976025c62451932b9b49bb.png
      @@ -1439,7 +1439,7 @@

      Visualizations -
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+
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 ../_images/6403f4edbc5ee6cf4d8e2d75a250d6174fea64bffc1a86b12ccfb44885e7b275.png
diff --git a/stats_overview/02_PROB.html b/stats_overview/02_PROB.html
index 1c877b36..37a0edfd 100644
--- a/stats_overview/02_PROB.html
+++ b/stats_overview/02_PROB.html
@@ -628,7 +628,7 @@ 
      Random process examples using Python
-
      0.12921002235829004
+
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@@ -665,7 +665,7 @@ 
      Random process examples using Python
-
      0.5046
+
      0.4939
 
      
 
      
 
      
@@ -685,7 +685,7 @@ 
      Random process examples using Python
-
      6
+
      2
 
      
 
      
 
      
@@ -700,19 +700,19 @@ 
      Random process examples using Python
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+
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      <Axes: >
 
      
 
      
-../_images/a6ba825cb62613bbb9b19e7531f85db0c08cf603cb2442591ec9e9ee382369e0.png
+../_images/8762a18fe84e2b0ba0e20403f6454d845785be82407216c4891f275a6f1602c0.png
 
      
 
      
 
      
@@ -778,7 +778,7 @@ 
      Uniform distribution
 
      
 
      
-
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+
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diff --git a/stats_overview/04_LINEAR_MODELS.html b/stats_overview/04_LINEAR_MODELS.html
index 05653f42..e7fcd5a0 100644
--- a/stats_overview/04_LINEAR_MODELS.html
+++ b/stats_overview/04_LINEAR_MODELS.html
@@ -800,10 +800,10 @@ 
      Using statsmodels formula API
-
      <pandas.core.groupby.generic.DataFrameGroupBy object at 0x7f513df91d90>
+
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diff --git a/tutorials/python_tutorial.html b/tutorials/python_tutorial.html
index 9e0a26ae..819c3f19 100644
--- a/tutorials/python_tutorial.html
+++ b/tutorials/python_tutorial.html
@@ -2918,7 +2918,7 @@ 
      Installing packages using 
 
      
 
      
-
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+
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 Requirement already satisfied: mpmath<1.4,>=1.1.0 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from sympy) (1.3.0)
 
      
 
      
diff --git a/tutorials/src/pycut_material.html b/tutorials/src/pycut_material.html
index ddb0684a..c23b25d6 100644
--- a/tutorials/src/pycut_material.html
+++ b/tutorials/src/pycut_material.html
@@ -1346,7 +1346,7 @@ 
      Defining new types of objects
-
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diff --git a/tutorials/src/python_tutorial_src.html b/tutorials/src/python_tutorial_src.html
index 3fe3e038..bfe050fa 100644
--- a/tutorials/src/python_tutorial_src.html
+++ b/tutorials/src/python_tutorial_src.html
@@ -3118,7 +3118,7 @@ 
      Installing packages using 
 
      
 
      
-
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+
      Requirement already satisfied: sympy in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (1.13.2)
 Requirement already satisfied: mpmath<1.4,>=1.1.0 in /opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages (from sympy) (1.3.0)