diff --git a/04_probability_distributions.ipynb b/04_probability_distributions.ipynb
index 1c50268..8a3791b 100644
--- a/04_probability_distributions.ipynb
+++ b/04_probability_distributions.ipynb
@@ -1413,7 +1413,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Measuring distances btween distributions\n",
+ "## Measuring distances between distributions\n",
"\n",
"There are several ways to measure distances between two probability distributions with PDFs $p(x)$ and $q(x)$, each with its own characteristics and applications. \n",
"\n",
diff --git a/05_Bayesian_inference.ipynb b/05_Bayesian_inference.ipynb
index 649f332..2cd9cdd 100644
--- a/05_Bayesian_inference.ipynb
+++ b/05_Bayesian_inference.ipynb
@@ -244,9 +244,9 @@
"\n",
"What does it take?\n",
"\n",
- "- `Data`\n",
- "- A generative model (how does the conditional `likelihood` come about?)\n",
- "- Our `beliefs` before seeing the data.\n",
+ "- Data,\n",
+ "- A generative model,\n",
+ "- Our beliefs before seeing the data.\n",
"\n",
"What does it make?\n",
"\n",
diff --git a/09_intro_to_Numpyro.ipynb b/09_intro_to_Numpyro.ipynb
index 0b1c907..1735f97 100644
--- a/09_intro_to_Numpyro.ipynb
+++ b/09_intro_to_Numpyro.ipynb
@@ -352,7 +352,7 @@
"`````{admonition} Task: Point estimates for Bernoulli-beta coin flips\n",
":class: tip\n",
"- You might have correctly noticed that we have not looked at the `Predictive` capability. Study the documentation of Numpyro (in particular, `numpyro.infer`) and demonstrate the `Predictive` command on the example shown above.\n",
- "- Study the documentation of Numpyro (in particular, `numpyro.diagnostics`) to undertand what the `hpdi` command does. Apply it to the example shown above.\n",
+ "- Study the documentation of Numpyro (in particular, `numpyro.diagnostics`) to understand what the `hpdi` command does. Apply it to the example shown above.\n",
"`````"
]
},
diff --git a/11_Bayesian_workflow.ipynb b/11_Bayesian_workflow.ipynb
new file mode 100644
index 0000000..e72a3be
--- /dev/null
+++ b/11_Bayesian_workflow.ipynb
@@ -0,0 +1,1211 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "J1LV5w4eFSzA"
+ },
+ "source": [
+ "# Bayesian workflow\n",
+ "\n",
+ "Leveraging Bayesian inference for addressing real-world problems requires from the modeller not only to be proficient in statsitics, have domain expertise and programming skills, but also a deep understanding of the decision-making process while analysing data. Apart from inference, the workflow includes iterative model building, model checking, validation and troubleshooting of computational problems, model understanding, and model comparison.\n",
+ "\n",
+ "Seemingly, the Bayes rule looks very simple:\n",
+ "\n",
+ "$$\\underbrace{p(\\theta|y)}_\\text{posterior} \\propto \\underbrace{p(y | \\theta)}_{\\text{likelihood}} \\underbrace{p(\\theta)}_{\\text{prior}}$$\n",
+ "\n",
+ "What could possibly go wrong about it in practice?\n",
+ "\n",
+ "A lot can go wrong! And in case things go wrong, decisions need to be made sequentially about model building and improvement. That is why we need the Bayesian workflow."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Principles of Bayesian workflow\n",
+ "\n",
+ "Workflows exist in a variety of disciplines where they define what is a 'good practice'.\n",
+ "\n",
+ "\n",
+ "## Box's loop\n",
+ "\n",
+ "In the 1960's, the statistician Box formulated the notion of a loop to understand the nature of the scientific method. This loop is called Box's loop by Blei et. al. (2014):\n",
+ "\n",
+ "\n",
+ "![](assets/boxes_loop.png)\n",
+ "\n",
+ "\n",
+ "## Modern Bayesian workflow\n",
+ "\n",
+ "A systematic review of the steps within the modern Bayesian workflow, described in Gelman et al. (2020):\n",
+ "\n",
+ "![](assets/bayes_workflow.png)\n",
+ "\n",
+ "## Prior predictive checks\n",
+ "\n",
+ "Prior predictive checking consists in simulating data from the priors. Then such simulations are commonly visualized (especially when transformations of parameters is involved). This shows the range of data compatible with the model, helps understand the adequacy of the chosen priors, as it is often easier to elicit expert knowledge on measureable quantities of interest rather than abstract parameter values.\n",
+ "\n",
+ "\n",
+ "## Iterative model building\n",
+ "\n",
+ "A possible realisation of the Bayeisan workflow loop:\n",
+ "\n",
+ "- Understand the domain and problem,\n",
+ "\n",
+ "- Formulate the model mathematically,\n",
+ "\n",
+ "- Implement model, test, debug,\n",
+ "\n",
+ "- debug, debug, debug.\n",
+ "\n",
+ "- Perform prior predictive, check,\n",
+ "\n",
+ "- Fit the model,\n",
+ "\n",
+ "- Assess convergence diagnostics,\n",
+ "\n",
+ "- Perform posterior predictive check, \n",
+ "\n",
+ "- Improve the model iteratively: from baseline to complex and computationally efficient models.\n",
+ "\n",
+ "## Examples\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/opt/anaconda3/envs/aims/lib/python3.9/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
+ " from .autonotebook import tqdm as notebook_tqdm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpyro\n",
+ "import numpyro.distributions as dist\n",
+ "from numpyro.infer import MCMC, NUTS, Predictive\n",
+ "from numpyro.diagnostics import hpdi\n",
+ "\n",
+ "import jax\n",
+ "import jax.numpy as jnp\n",
+ "from jax import random\n",
+ "\n",
+ "import arviz as az\n",
+ "from scipy.stats import gaussian_kde\n",
+ "\n",
+ "import matplotlib.pyplot as plt\n",
+ "import pandas as pd\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Coin tossing "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 100 # number of trials\n",
+ "h = 61 # number of successes\n",
+ "alpha = 2 # hyperparameters\n",
+ "beta = 2\n",
+ "\n",
+ "niter = 1000"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Model"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "```{margin}\n",
+ "Note `h=None` here. If we pass data for `h`, inference will be performed by conditioning on this data. Otherwise we will obtain prior predictive samples.\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def model(n, alpha=2, beta=2, h=None):\n",
+ "\n",
+ " # prior on the probability of success p\n",
+ " p = numpyro.sample('p', dist.Beta(alpha, beta))\n",
+ "\n",
+ " # likelihood - notice the `obs=h` part\n",
+ " # p is the probabiity of success,\n",
+ " # n is the total number of experiments\n",
+ " # h is the number of successes\n",
+ " numpyro.sample('obs', dist.Binomial(n, p), obs=h)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Prior Predictive check"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rng_key = random.PRNGKey(0)\n",
+ "rng_key, rng_key_ = random.split(rng_key)\n",
+ "\n",
+ "# use the Predictive class to generate predictions.\n",
+ "# Notice that we are not passing observation `h` as data.\n",
+ "# Since we have set `h=None`, this allows the model to make predictions of `h`\n",
+ "# when data for it is not provided.\n",
+ "prior_predictive = Predictive(model, num_samples=1000)\n",
+ "prior_predictions = prior_predictive(rng_key_, n)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "dict_keys(['obs', 'p'])"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# we have generated samples for two variables\n",
+ "prior_predictions.keys()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# extract samples for variable 'p'\n",
+ "pred_obs = prior_predictions['p']\n",
+ "\n",
+ "# compute its summary statistics for the samples of `p`\n",
+ "mean_prior_pred = jnp.mean(pred_obs, axis=0)\n",
+ "hpdi_prior_pred = hpdi(pred_obs, 0.89)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig = plt.figure(dpi=100, figsize=(5, 3))\n",
+ "plt.hist(pred_obs, bins=15, density=True, alpha=0.5, color='teal')\n",
+ "x = jnp.linspace(0, 1, 3000)\n",
+ "kde = gaussian_kde(pred_obs)\n",
+ "plt.plot(x, kde(x), color='teal', lw=3, alpha=0.5)\n",
+ "plt.xlabel('p')\n",
+ "plt.title('Prior predictive distribution for $p$')\n",
+ "plt.xlim(0, 1)\n",
+ "plt.grid(0.3)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Inference\n",
+ "\n",
+ "Using the same routine as we did for prior redictive, we can perform inference by using the observed data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ ":8: UserWarning: There are not enough devices to run parallel chains: expected 4 but got 1. Chains will be drawn sequentially. If you are running MCMC in CPU, consider using `numpyro.set_host_device_count(4)` at the beginning of your program. You can double-check how many devices are available in your system using `jax.local_device_count()`.\n",
+ " mcmc = MCMC(kernel, num_warmup=1000, num_samples=2000, num_chains=4, progress_bar=False)\n"
+ ]
+ }
+ ],
+ "source": [
+ "rng_key = random.PRNGKey(0)\n",
+ "rng_key, rng_key_ = random.split(rng_key)\n",
+ "\n",
+ "# specify inference algorithm\n",
+ "kernel = NUTS(model)\n",
+ "\n",
+ "# define number of samples and number chains\n",
+ "mcmc = MCMC(kernel, num_warmup=1000, num_samples=2000, num_chains=4, progress_bar=False)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#run MCMC\n",
+ "mcmc.run(rng_key_, n=n, h=h)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# exatract samples of parameter p\n",
+ "p_samples = mcmc.get_samples()\n",
+ "p_posterior_samples = p_samples['p']"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig = plt.figure(dpi=100, figsize=(5, 3))\n",
+ "plt.hist(pred_obs, bins=15, density=True, alpha=0.5, color='teal', label = \"Prior distribution\")\n",
+ "plt.hist(p_posterior_samples, bins=15, density=True, alpha=0.5, color='orangered', label = \"Posterior distribution\")\n",
+ "x = jnp.linspace(0, 1, 3000)\n",
+ "kde = gaussian_kde(pred_obs)\n",
+ "plt.plot(x, kde(x), color='teal', lw=3, alpha=0.5)\n",
+ "kde = gaussian_kde(p_posterior_samples)\n",
+ "plt.plot(x, kde(x), color='orangered', lw=3, alpha=0.5)\n",
+ "plt.xlabel('p')\n",
+ "plt.xlim(0, 1)\n",
+ "plt.grid(0.3)\n",
+ "plt.legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Check convergence\n",
+ "\n",
+ "We now have obtained the samples from MCMC. How can we assess whether we can trust the results? Convergence diganostics survey this purpose. Beyond $\\hat{R}$, we can also visually inspect traceplots. Traceplots are simply sample values plotted against the iteration number. We want those traceplots to be stationary, i.e. they should look like a \"hairy carterpillar\"."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " mean std median 5.0% 95.0% n_eff r_hat\n",
+ " p 0.61 0.05 0.61 0.53 0.68 3059.08 1.00\n",
+ "\n",
+ "Number of divergences: 0\n"
+ ]
+ }
+ ],
+ "source": [
+ "# inpect summary\n",
+ "# pring summary and look at R-hat\n",
+ "# r_hat is a dignostic comparing within chain variation to between chan variation.\n",
+ "# It is an importnat convergene diagnostic, and we want its valye to be close to 1\n",
+ "mcmc.print_summary()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot posterior distribution and traceplots\n",
+ "data = az.from_numpyro(mcmc)\n",
+ "az.plot_trace(data, compact=True);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Posterior predictive distribution\n",
+ "\n",
+ "The posterior predictive distribution is a concept in Bayesian statistics that combines the information from both the observed data and the posterior distribution of model parameters to generate predictions for new, unseen data .\n",
+ "\n",
+ "We can use the obtained samples obtained at the previous step to generate posterior predictive desitribution on the outcome."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# using the same 'Predictive' class,\n",
+ "# but now specifying also `p_samples`\n",
+ "rng_key, rng_key_ = random.split(rng_key)\n",
+ "predictive = Predictive(model, p_samples)\n",
+ "posterior_predictions = predictive(rng_key_, n=n)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# extract prediction and calculate summary statistics\n",
+ "post_obs = posterior_predictions['obs']\n",
+ "mean_post_pred = jnp.mean(post_obs, axis=0)\n",
+ "hpdi_post_pred = hpdi(post_obs, 0.9)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Array(60.508003, dtype=float32)"
+ ]
+ },
+ "execution_count": 16,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# what is the mean number of successes?\n",
+ "mean_post_pred"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([48, 70], dtype=int32)"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# what is the unceratinty around this mean?\n",
+ "hpdi_post_pred"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Group task:** change the hyperparamaters of the model. How are they changing the results?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bayesian Linear regression\n",
+ "\n",
+ "Now that we know how to use NumPyro. Let us build an example using larger amounts of data and build a Bayesian Linear Regression model. It is the same Linear Regression model you are familiar with, but here all of the parameters are estimated in the Bayesian way."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "--2024-03-19 22:17:00-- https://raw.githubusercontent.com/deep-learning-indaba/indaba-pracs-2023/main/data/Howell1.csv\n",
+ "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.111.133, 185.199.108.133, 185.199.109.133, ...\n",
+ "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.111.133|:443... connected.\n",
+ "HTTP request sent, awaiting response... 200 OK\n",
+ "Length: 12205 (12K) [text/plain]\n",
+ "Saving to: ‘Howell1.csv’\n",
+ "\n",
+ "Howell1.csv 100%[===================>] 11.92K --.-KB/s in 0.002s \n",
+ "\n",
+ "2024-03-19 22:17:00 (5.75 MB/s) - ‘Howell1.csv’ saved [12205/12205]\n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "text/html": [
+ "
"
+ ],
+ "text/plain": [
+ " weight_pred mean_pred lower upper\n",
+ "0 45 154.772690 139.393387 169.614548\n",
+ "1 40 146.176010 131.200302 161.135223\n",
+ "2 65 190.045502 175.474350 204.991074\n",
+ "3 31 130.221954 115.344894 145.279709\n",
+ "4 53 168.721436 154.352890 184.339874"
+ ]
+ },
+ "execution_count": 31,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# predict for new data\n",
+ "predictive = Predictive(model, samples_1)\n",
+ "predictions = predictive(rng_key_, weight=weight_pred)['obs']\n",
+ "\n",
+ "mean_pred = jnp.mean(predictions, axis=0)\n",
+ "hpdi_pred = hpdi(predictions, 0.89)\n",
+ "\n",
+ "d = {'weight_pred': weight_pred, 'mean_pred': mean_pred, 'lower': hpdi_pred[0,], 'upper': hpdi_pred[1,]}\n",
+ "df_res = pd.DataFrame(data=d)\n",
+ "df_res.head()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`````{admonition} Task\n",
+ ":class: tip\n",
+ "Modify the model so that it fits better. \n",
+ "\n",
+ "**Hint:** apply a transformation to input data, e.g. a polynomial.\n",
+ "\n",
+ "For this model, \n",
+ "\n",
+ "- plot prior predictive distribution,\n",
+ "- perform inference,\n",
+ "- plot posterior predictive dsitribution.\n",
+ "`````\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Model comparison\n",
+ "\n",
+ "It often occurrs in practice that we have several model candidates at hand and need to choose the best model for the given data.\n",
+ "\n",
+ "It is a tricky task, since increasing model complexity typically leads to improved data fitting by introducing more parameters, creating the the risk of overfitting.\n",
+ "\n",
+ "Hence, the models we are looking for, should not just describe well the observed data, but, ideally, the entire \"true\" data generating process. We need to find tools to quantify the degree of “closeness” to the true model. Note that in this context models refer to the distributional family as well as the parameter values.\n",
+ "\n",
+ "We could use KLD to measure the degree of “closeness” between two models $M_0$ and $M_1$:\n",
+ "\n",
+ "$$\n",
+ "\\text{KLD}(M_0 \\parallel M_1) = \\int p_{M_0}(y) \\log \\left( \\frac{p_{M_0}(y)}{p_{M_1}(y)} \\right) dy = \\int p_{M_0}(y) \\log p_{M_0}(y) dy - \\int p_{M_0}(y) \\log p_{M_1}(y) dy\n",
+ "$$\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`````{admonition} Task \n",
+ ":class: tip\n",
+ "\n",
+ "Assume that the 'true' model $M_0$ and the two candidate modelas are $M_1$ and $M_2$\n",
+ "\n",
+ "- $M_0: y \\sim \\mathcal{N}(3,2)$\n",
+ "- $M_1: y \\sim \\mathcal{N}(3.5,2.5)$\n",
+ "- $M_2: y \\sim \\text{Cauchy}(3,2)$\n",
+ "\n",
+ "For these models,\n",
+ "\n",
+ "- Compute divergences $\\text{KLD}(M_0 \\parallel M_1)$, $\\text{KLD}(M_0 \\parallel M_2)$\n",
+ "- Which model is better: $M_1$ or $M_2$?\n",
+ "\n",
+ "`````"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that the first term in $\\text{KLD}(M_0 \\parallel M_1)$ is always the same. Hence, we only need to compare models on the second term $\\int p_{M_0}(y) \\log p_{M_1}(y) dy$, which is the expected log predictive density (elpd):\n",
+ "\n",
+ " $$\n",
+ " \\int p_{M_0}(y) \\log p_{M_1}(y) dy = \\mathbb{E}[ \\log p_{M_1}].\n",
+ " $$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The problem we have here is taht in reality we never know the true model $M_0.$ Several numerical metrics are commonly used for this purpose in the literature such as infromation criteria and cross validation.\n",
+ "\n",
+ "### Informtation criteria\n",
+ "\n",
+ "Akaike Information Criterion (AIC)\n",
+ " \n",
+ "$$\n",
+ "\\text{AIC} = - 2 l(\\hat{\\theta}_\\text{MLE}) + 2p,\n",
+ "$$\n",
+ "\n",
+ "where $l$ is the log-likelihood, $p$ is the number of parameters and $\\theta_\\text{MLE}$ is the MLE estimate.\n",
+ "\n",
+ "A lower AIC value indicates a better trade-off between model fit and complexity, implying a better model.\n",
+ "\n",
+ "AIC works best when the probability distribution under $M_1$ is normal, and the sample size is much larger than the number of parameters. No posterior distribution is used, as $D$ is computed only based on the MLE. It does not take into account any prior information.\n",
+ "\n",
+ "Bayesian Information Criterion (AIC)\n",
+ "\n",
+ "$$\n",
+ "\\text{BIC} = - 2 l(\\hat{\\theta}_\\text{MLE}) + p \\ln(n),\n",
+ "$$\n",
+ "\n",
+ "where $n$ is the number of datapoints.\n",
+ "\n",
+ "BIC is derived using the Laplace approximation. It is only valid for sample size $n$ much larger than the number $p$ of parameters in the model. The BIC is independent of the prior and generally penalizes free parameters more strongly than the Akaike information criterion, though it depends on the size of $n$ and relative magnitude of $n$ and $k$.\n",
+ "\n",
+ "Watanabe-Akaike Information Criteria (WAIC)\n",
+ "\n",
+ "$$\n",
+ "\\begin{align*}\n",
+ "\\text{WAIC} = &- 2 \\sum_{i=1}^{n} \\log \\mathbb{E}[p(y_i | \\theta, y)] + 2p_\\text{WAIC} \\\\\n",
+ " &-2 \\left( \\sum_{i=1}^{n} \\log \\left( \\frac{1}{S} \\sum_{s=1}^{S} p(y_i|\\theta_s) \\right) - \\sum_{i=1}^{n} \\text{Var}_s \\left( \\log p(y_i|\\theta_s) \\right) \\right)\n",
+ "\\end{align*}\n",
+ "$$\n",
+ "\n",
+ "where $ \\mathbb{E}[p(y_i | \\theta, y)]$ is the posterior mean of the likelihood of the $i$-th observation, $n$ is the number of data points, $S$ is the number of posterior samples.\n",
+ "\n",
+ "The WAIC incorporates prior information, and the use of pointwise likelihood makes it more robust when the posterior distributions deviate from normality."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Leave-One-Out Cross Validation\n",
+ "\n",
+ "Cross validation splits the current sample into $k$ parts. Then a model is being fit on $k−1$ parts and the predictions are make for the remaiining $1$ part.\n",
+ "\n",
+ "A special case is when $k=N$ so that each time one uses $N- 1$ data points to estimate the model parameters, and estimate the elpd for the observation that was left out. This is called leave-one-out cross-validation (LOO-CV). See [Vehrari, Gelman, Gabry (2016)](https://arxiv.org/pdf/1507.04544.pdf) for the details of how LOO elpd can be estomated from samples.\n",
+ "\n",
+ "\n",
+ "We can use tools from `arviz` library to help us [perform model comparison](https://python.arviz.org/en/latest/examples/plot_compare.html)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "`````{admonition} Task \n",
+ ":class: tip\n",
+ "\n",
+ "Download the `kidiq` dataset (Gelman & Hill, 2007), which is data from a survey of adult American women and their respective children. Dated from 2007, it has 434 observations and 4 variables:\n",
+ "\n",
+ "- `kid_score`: child's IQ\n",
+ "\n",
+ "- `mom_hs`: binary/dummy (0 or 1) if the child's mother has a high school diploma\n",
+ "\n",
+ "- `mom_iq`: mother's IQ\n",
+ "\n",
+ "- `mom_age`: mother's age\n",
+ "\n",
+ "with \n",
+ "\n",
+ "```\n",
+ "import pandas as pd\n",
+ "\n",
+ "!wget -O kidiq.csv https://github.com/TuringLang/TuringGLM.jl/raw/main/data/kidiq.csv\n",
+ "\n",
+ "df = pd.read_csv('kidiq.csv')\n",
+ "```\n",
+ "\n",
+ "Construct a model predicting model predicting `kid_score`:\n",
+ "\n",
+ "$$\n",
+ "\\text{kidscore}_i \\sim \\mathcal{N}(\\mu_i, \\sigma),\n",
+ "$$\n",
+ "\n",
+ "- Construct several model of $\\mu_i$ using the available predictors. \n",
+ "\n",
+ "- What models have you tried and which models performed the best?\n",
+ "\n",
+ "`````\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": []
+ }
+ ],
+ "metadata": {
+ "colab": {
+ "provenance": []
+ },
+ "kernelspec": {
+ "display_name": "Python 3",
+ "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": "3.9.18"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/999_acknowledgements.md b/999_acknowledgements.md
index 270127e..0bbe0ca 100644
--- a/999_acknowledgements.md
+++ b/999_acknowledgements.md
@@ -3,6 +3,7 @@
## Acknowledgements and links
- AIMS and Ulrich personally for the invitation
- [Machine Learning and Global Health](mlgh.net/people) network for many things, but in particular for the (virtual, at the time) space where I learnt Numpyro through a reading group together with some MLGH members: Swapnil Mishra, Iwona Hawryluk, Tim Wolock, Theo Rashid, Giovanni Charles
+- [Deep Learning Indaba](https://deeplearningindaba.com/) for showing me how much ML enthisuams there is on the African continent and making me want to contribute
- Co-authors of the paper [Bayesian workflow for disease transmission modeling in Stan](https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.9164) and all particiapnts of the regular Thursday Stan call which enabled me to co-author
- Lorenzo Ciardo from Kellogg College at Oxford for telling me about the Buffon's needle problem
- Richard McEarlth for posting the [prior-likelihood conflict example](https://twitter.com/rlmcelreath/status/1701165075493470644)
diff --git a/_toc.yml b/_toc.yml
index 64e8041..a0d7441 100644
--- a/_toc.yml
+++ b/_toc.yml
@@ -13,4 +13,5 @@ chapters:
- file: 08_PPLs.ipynb
- file: 09_intro_to_Numpyro.ipynb
- file: 10_focus_on_priors.ipynb
+- file: 11_Bayesian_workflow.ipynb
- file: 999_acknowledgements.md
\ No newline at end of file
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