deploy: 00f9a86

minireference · Aug 21, 2024 · 5fca638 · 5fca638
1 parent 9cc67c7
commit 5fca638
Show file tree

Hide file tree

Showing 116 changed files with 12,462 additions and 1,607 deletions.
diff --git a/_images/1653eb3ef0ddc25899b3197f96e7367594c4fe180aafd76872786fb91d873f5c.png b/_images/1653eb3ef0ddc25899b3197f96e7367594c4fe180aafd76872786fb91d873f5c.png
diff --git a/_images/177d412a04ceb10fa9c484d9973a2e95022cecb8b2182df55c77a05d85cdff8b.png b/_images/177d412a04ceb10fa9c484d9973a2e95022cecb8b2182df55c77a05d85cdff8b.png
diff --git a/_images/192bba20ecdae7da9fd6a15e53a6077b9e01a9e3fdc7f48b22652b3a789eb867.png b/_images/192bba20ecdae7da9fd6a15e53a6077b9e01a9e3fdc7f48b22652b3a789eb867.png
diff --git a/_images/193d8b4f98ddb39473f3be68613bbc19c5b61c184e042e365b5f87ac3afadcd9.png b/_images/193d8b4f98ddb39473f3be68613bbc19c5b61c184e042e365b5f87ac3afadcd9.png
diff --git a/_images/1b9740419120924fb9e3bfd519a61117ca1fbfc349dfd752b92786a539efbb19.png b/_images/1b9740419120924fb9e3bfd519a61117ca1fbfc349dfd752b92786a539efbb19.png
diff --git a/_images/1dfd788426c9ce57e6cda198a3dd9423e8494c49e0716c01c5bb02d8d4873750.png b/_images/1dfd788426c9ce57e6cda198a3dd9423e8494c49e0716c01c5bb02d8d4873750.png
diff --git a/_images/1dfe18d065c7cd84fa9f8c77c33fcd0a44aa19182ee4620439b51efec08f3fd4.png b/_images/1dfe18d065c7cd84fa9f8c77c33fcd0a44aa19182ee4620439b51efec08f3fd4.png
diff --git a/_images/22c1c3084644beeccda4e7381da3acb8d10c048a664f14ceb4c50ca36583c008.png b/_images/22c1c3084644beeccda4e7381da3acb8d10c048a664f14ceb4c50ca36583c008.png
diff --git a/_images/234e333f3f94654185f3faa9f97feba09779c36fd9b08afe20ec735e609e96d4.png b/_images/234e333f3f94654185f3faa9f97feba09779c36fd9b08afe20ec735e609e96d4.png
diff --git a/_images/2e3d8beb219883bceb9c616f611e78cfe672ac46328642af2d01cff669be171d.png b/_images/2e3d8beb219883bceb9c616f611e78cfe672ac46328642af2d01cff669be171d.png
diff --git a/_images/31e2731e5a95bc2c8d59967178a6a385e2b448df6be960a8095a678421c76415.png b/_images/31e2731e5a95bc2c8d59967178a6a385e2b448df6be960a8095a678421c76415.png
diff --git a/_images/336e553b1e15c6958c59d00722972a35abb626fae85ff3523b0a40d5ca975f06.png b/_images/336e553b1e15c6958c59d00722972a35abb626fae85ff3523b0a40d5ca975f06.png
diff --git a/_images/3681a00cf3324700010f095221675e9f5da4272b07b810bce1f19ba8856f7fc1.png b/_images/3681a00cf3324700010f095221675e9f5da4272b07b810bce1f19ba8856f7fc1.png
diff --git a/_images/368cd8393957ad84ef9c4e00c5e06905d7314f306a9c5e44a5e8fadf92ae183a.png b/_images/368cd8393957ad84ef9c4e00c5e06905d7314f306a9c5e44a5e8fadf92ae183a.png
diff --git a/_images/3b2196e33cc62cd5355a0cc40146bc4e09ba61c5e38c2fae348ccfc7dfb13548.png b/_images/3b2196e33cc62cd5355a0cc40146bc4e09ba61c5e38c2fae348ccfc7dfb13548.png
diff --git a/_images/4224a65fac69276abb3c4935776681bc0f66bdb11e863e715d5e480fd9475302.png b/_images/4224a65fac69276abb3c4935776681bc0f66bdb11e863e715d5e480fd9475302.png
diff --git a/_images/45666da5d85d1eee587014c83b1b0d0fd478e1e6a12d267500b86e562746c567.png b/_images/45666da5d85d1eee587014c83b1b0d0fd478e1e6a12d267500b86e562746c567.png
diff --git a/_images/48e6f6f246e89e886ce68a26fb833ad5cc01f9bda1ddd94513126cada2cb9700.png b/_images/48e6f6f246e89e886ce68a26fb833ad5cc01f9bda1ddd94513126cada2cb9700.png
diff --git a/_images/51d4928fb5d591a7955d1b5f8373cf5dec6a1455213dde233136ef86d9b37ee1.png b/_images/51d4928fb5d591a7955d1b5f8373cf5dec6a1455213dde233136ef86d9b37ee1.png
diff --git a/_images/578fac1f096b9a2cc93e2d3e9a04dbe5a2bf52af6823d63ffe5aa79f4c45d486.png b/_images/578fac1f096b9a2cc93e2d3e9a04dbe5a2bf52af6823d63ffe5aa79f4c45d486.png
diff --git a/_images/62ba2e79c0bd4b398418659edc46860ad1668e9bef41920a2052e7ecf52e6537.png b/_images/62ba2e79c0bd4b398418659edc46860ad1668e9bef41920a2052e7ecf52e6537.png
diff --git a/_images/649b4326f67ce9cd1bad270b86a168b435beeaa49407757bfa9b59f49551203c.png b/_images/649b4326f67ce9cd1bad270b86a168b435beeaa49407757bfa9b59f49551203c.png
diff --git a/_images/66007abe13528ce102c2b15016aa9fbc57e9e665399407160b4a8624bac71301.png b/_images/66007abe13528ce102c2b15016aa9fbc57e9e665399407160b4a8624bac71301.png
diff --git a/_images/667f3c660c0ddb4edc790c61a2e966ad0188daf5d9a1ae25dca78bc55dc5137a.png b/_images/667f3c660c0ddb4edc790c61a2e966ad0188daf5d9a1ae25dca78bc55dc5137a.png
diff --git a/_images/6ae57cd57c2eb686319db6f4eb8ac72be9125de872ca88b6d230e1e655ac13e4.png b/_images/6ae57cd57c2eb686319db6f4eb8ac72be9125de872ca88b6d230e1e655ac13e4.png
diff --git a/_images/7037635c81105b3b63caa1767e533482a4d9d79863285f5b1b3effbb51090082.png b/_images/7037635c81105b3b63caa1767e533482a4d9d79863285f5b1b3effbb51090082.png
diff --git a/_images/75222ba72d4da78606636f9fa330fb97975d28eace85c044d78b75e66e2c4353.png b/_images/75222ba72d4da78606636f9fa330fb97975d28eace85c044d78b75e66e2c4353.png
diff --git a/_images/75d349e59235c0448022b23e35e53bf0bde5fadc4a0829ebfccad4862d3c5208.png b/_images/75d349e59235c0448022b23e35e53bf0bde5fadc4a0829ebfccad4862d3c5208.png
diff --git a/_images/7774bcf673a90801d096af56c75b8ade966e5d4951761b7c8fa5e97f6fef5aee.png b/_images/7774bcf673a90801d096af56c75b8ade966e5d4951761b7c8fa5e97f6fef5aee.png
diff --git a/_images/77b8dddda53b94cfbb8c1ab358072b2fbff2eb97114c00aa7b281f5ed3b0ebc3.png b/_images/77b8dddda53b94cfbb8c1ab358072b2fbff2eb97114c00aa7b281f5ed3b0ebc3.png
diff --git a/_images/80c5529eb521d25833f837d0e232c29b93f5154f6b867f07b377170b6e64debf.png b/_images/80c5529eb521d25833f837d0e232c29b93f5154f6b867f07b377170b6e64debf.png
diff --git a/_images/80c6c3824d8a8799edbb0f340cc28b90bf5d8925c3dbdfa78667d9ade095e1a3.png b/_images/80c6c3824d8a8799edbb0f340cc28b90bf5d8925c3dbdfa78667d9ade095e1a3.png
diff --git a/_images/86f4c65cc9db7d0c88f506afc49406bd0ade3ae93bf3875a69bc245227a9e683.png b/_images/86f4c65cc9db7d0c88f506afc49406bd0ade3ae93bf3875a69bc245227a9e683.png
diff --git a/_images/8762a18fe84e2b0ba0e20403f6454d845785be82407216c4891f275a6f1602c0.png b/_images/8762a18fe84e2b0ba0e20403f6454d845785be82407216c4891f275a6f1602c0.png
diff --git a/_images/926593044408511881c40a380b122f40852e750b662642f9ce787433f71e3fee.png b/_images/926593044408511881c40a380b122f40852e750b662642f9ce787433f71e3fee.png
diff --git a/_images/93b781a05ec28ddc6351a24c5908f716ae99a7f6e8fada7880c48a265bf78c90.png b/_images/93b781a05ec28ddc6351a24c5908f716ae99a7f6e8fada7880c48a265bf78c90.png
diff --git a/_images/984dd7f8d91a8ed7563622bc958a47fb16fcb896b19c2135f4653157d253f488.png b/_images/984dd7f8d91a8ed7563622bc958a47fb16fcb896b19c2135f4653157d253f488.png
diff --git a/_images/9955cb3ab979ab8221c4f60919b7f132690d4171ea8b126888a3ca62cf27ea6c.png b/_images/9955cb3ab979ab8221c4f60919b7f132690d4171ea8b126888a3ca62cf27ea6c.png
diff --git a/_images/9fd5360e7d876977cb477810a80f270dbd85191d86aab65f74e3a9086e9d2bf2.png b/_images/9fd5360e7d876977cb477810a80f270dbd85191d86aab65f74e3a9086e9d2bf2.png
diff --git a/_images/a1191a35129b911e90ba286cf81891e47b38d1273ed51685304e6edc11f32126.png b/_images/a1191a35129b911e90ba286cf81891e47b38d1273ed51685304e6edc11f32126.png
diff --git a/_images/a6ba825cb62613bbb9b19e7531f85db0c08cf603cb2442591ec9e9ee382369e0.png b/_images/a6ba825cb62613bbb9b19e7531f85db0c08cf603cb2442591ec9e9ee382369e0.png
diff --git a/_images/a8664b40fd1f1c5d76f5a759a3956d463793dc66e0976025c62451932b9b49bb.png b/_images/a8664b40fd1f1c5d76f5a759a3956d463793dc66e0976025c62451932b9b49bb.png
diff --git a/_images/aa554fd940665088ca108d40500d3437e7d882788ae25b3dc1652c11a54d6f04.png b/_images/aa554fd940665088ca108d40500d3437e7d882788ae25b3dc1652c11a54d6f04.png
diff --git a/_images/ab84b393ebb4e1b01a697cf1bc37ca509b8b11f82d3487d55fb4cb87099abc3f.png b/_images/ab84b393ebb4e1b01a697cf1bc37ca509b8b11f82d3487d55fb4cb87099abc3f.png
diff --git a/_images/b28d68010962f93796c68430f56b4fd2202e9fb21861cd75c5932b76301b42cc.png b/_images/b28d68010962f93796c68430f56b4fd2202e9fb21861cd75c5932b76301b42cc.png
diff --git a/_images/b666ee31a98e09ac6daa8364b7185f0a9317d9bd7e5d70b45c12df60132d4083.png b/_images/b666ee31a98e09ac6daa8364b7185f0a9317d9bd7e5d70b45c12df60132d4083.png
diff --git a/_images/b92e7f6ce01cf87a7552dca25fba905bea4f92617dc1c5240a30cb3fa099eb75.png b/_images/b92e7f6ce01cf87a7552dca25fba905bea4f92617dc1c5240a30cb3fa099eb75.png
diff --git a/_images/bcfb2439bc15fbc7d378ccad8f002e88312aea6081a9a5a47085a7cf5deac4da.png b/_images/bcfb2439bc15fbc7d378ccad8f002e88312aea6081a9a5a47085a7cf5deac4da.png
diff --git a/_images/bd2bd272719ce132266d37adb340c89f3c3d5c06a3434e7adfbcb0084e373a28.png b/_images/bd2bd272719ce132266d37adb340c89f3c3d5c06a3434e7adfbcb0084e373a28.png
diff --git a/_images/bf7fd9435be6ed01b7b11fbe8242df0666f61e30a04d9f746bcbaee1f946cbc0.png b/_images/bf7fd9435be6ed01b7b11fbe8242df0666f61e30a04d9f746bcbaee1f946cbc0.png
diff --git a/_images/c35dbfab062b61a772db592a5c9640512818003e1017db9f72eb9b82e484ecc8.png b/_images/c35dbfab062b61a772db592a5c9640512818003e1017db9f72eb9b82e484ecc8.png
diff --git a/_images/c64dd0bf274b681c19946a9eb317bc7cfc915eeb7152b7cea5deae87e904f95f.png b/_images/c64dd0bf274b681c19946a9eb317bc7cfc915eeb7152b7cea5deae87e904f95f.png
diff --git a/_images/c961c561af9d17021ad227e137826aa831fa034f668dec63cd26fc29dc3aaa07.png b/_images/c961c561af9d17021ad227e137826aa831fa034f668dec63cd26fc29dc3aaa07.png
diff --git a/_images/caa638a3c0703dd601255b9c6714f15b0bb7651c33a5e096f87b79a19ab1117a.png b/_images/caa638a3c0703dd601255b9c6714f15b0bb7651c33a5e096f87b79a19ab1117a.png
diff --git a/_images/d39e6b60d9ac4d4790c082b3889e86bb422068c5aff44e4fcc075fc60a1a6008.png b/_images/d39e6b60d9ac4d4790c082b3889e86bb422068c5aff44e4fcc075fc60a1a6008.png
diff --git a/_images/d3d691c99f489baeb4ffd5ab63652dfe9a4c7a6d103841d9e39f77892f3a5ec3.png b/_images/d3d691c99f489baeb4ffd5ab63652dfe9a4c7a6d103841d9e39f77892f3a5ec3.png
diff --git a/_images/d7a4ae8a998f4cb89c56d709ecf787c03178bb6afea6843720bb0a8c4435568b.png b/_images/d7a4ae8a998f4cb89c56d709ecf787c03178bb6afea6843720bb0a8c4435568b.png
diff --git a/_images/d925d1082c879f5cb5872c8d1a7468ca6373c171970feb1e61669388eb0483e6.png b/_images/d925d1082c879f5cb5872c8d1a7468ca6373c171970feb1e61669388eb0483e6.png
diff --git a/_images/d9a3b5f6671ab61689cce12eff733cbe0ed37f1ac3ad727a488eb7ec01998e7b.png b/_images/d9a3b5f6671ab61689cce12eff733cbe0ed37f1ac3ad727a488eb7ec01998e7b.png
diff --git a/_images/dadfab5ad78222d36e5a0c6495b79548e8c1df1228d8ece7bd71344cca75b162.png b/_images/dadfab5ad78222d36e5a0c6495b79548e8c1df1228d8ece7bd71344cca75b162.png
diff --git a/_images/dc3975407047c1d030324b818ec6657508ac98b72cc9712e26b4838e09323ee7.png b/_images/dc3975407047c1d030324b818ec6657508ac98b72cc9712e26b4838e09323ee7.png
diff --git a/_images/de2813702a2bcd8a6afc5394198dd38c45af724236d7fae75f7a6ef8324348c5.png b/_images/de2813702a2bcd8a6afc5394198dd38c45af724236d7fae75f7a6ef8324348c5.png
diff --git a/_images/e07388f26065ab89313423889d8bb54043efa1b3bc97aa6974c407819bd11d17.png b/_images/e07388f26065ab89313423889d8bb54043efa1b3bc97aa6974c407819bd11d17.png
diff --git a/_images/e5ca810b7a619cd61276e9a555c92d21608dd6ccd46eb9dec891ed031d5dbaed.png b/_images/e5ca810b7a619cd61276e9a555c92d21608dd6ccd46eb9dec891ed031d5dbaed.png
diff --git a/_images/e63a46c024d5db7b2880aeca1cbde9ca9fac69c6095b4a1ef90cf2507306794b.png b/_images/e63a46c024d5db7b2880aeca1cbde9ca9fac69c6095b4a1ef90cf2507306794b.png
diff --git a/_images/e904336ae6943df01a21ef586cbe3d0f84d273468f29306f87d03e9e0c75845c.png b/_images/e904336ae6943df01a21ef586cbe3d0f84d273468f29306f87d03e9e0c75845c.png
diff --git a/_images/ebbe265d329064a88633b098c5a55e447392feeed8646eaaee49d53bb22cbc18.png b/_images/ebbe265d329064a88633b098c5a55e447392feeed8646eaaee49d53bb22cbc18.png
diff --git a/_images/f4dd33cf27a95e819664fe10fb012825babb0f0fff0019d4ea1564cfd13b583c.png b/_images/f4dd33cf27a95e819664fe10fb012825babb0f0fff0019d4ea1564cfd13b583c.png
diff --git a/_images/f5df2a5b34d3ca25ad9b4a183a3d07ad2b72350c579fdd4d58edd4549df0682c.png b/_images/f5df2a5b34d3ca25ad9b4a183a3d07ad2b72350c579fdd4d58edd4549df0682c.png
diff --git a/_images/fe6bdb18359b5bc084d572c11aa115df8a403c44e1174e56f3e69f2934b98ec7.png b/_images/fe6bdb18359b5bc084d572c11aa115df8a403c44e1174e56f3e69f2934b98ec7.png
diff --git a/_sources/notebooks/46_generalized_linear_models.ipynb b/_sources/notebooks/46_generalized_linear_models.ipynb
diff --git a/_sources/notebooks/50_extra_bayesian_stuff.ipynb 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",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
+       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='12000' class='' max='12000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [12000/12000 00:06&lt;00:00 Sampling 4 chains, 0 divergences]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "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",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
+       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='8000' class='' max='8000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [8000/8000 00:00&lt;00:00]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "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