{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Running on PyMC v5.27.0+57.g9ffda82e0.dirty\n"
]
}
],
"source": [
"import arviz as az\n",
"import numpy as np\n",
"\n",
"import pymc as pm\n",
"\n",
"print(f\"Running on PyMC v{pm.__version__}\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"az.style.use(\"arviz-variat\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(model_comparison)=\n",
"# Model comparison\n",
"\n",
"To demonstrate the use of model comparison criteria in PyMC, we implement the **8 schools** example from Section 5.5 of Gelman et al (2003), which attempts to infer the effects of coaching on SAT scores of students from 8 schools. Below, we fit a **pooled model**, which assumes a single fixed effect across all schools, and a **hierarchical model** that allows for a random effect that partially pools the data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The data include the observed treatment effects (`y`) and associated standard deviations (`sigma`) in the 8 schools."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"y = np.array([28, 8, -3, 7, -1, 1, 18, 12])\n",
"sigma = np.array([15, 10, 16, 11, 9, 11, 10, 18])\n",
"J = len(y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Pooled model"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [mu]\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "bd7fbd2e2a6a4fcd80bf4d70b383a0bd",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Output()"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_trace_dist(trace_p);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Hierarchical model"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [eta, mu, tau]\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "6246a578adde4373a319a75b165bf895",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Output()"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_trace_dist(trace_h, var_names=\"mu\");"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_forest(trace_h, var_names=\"theta\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Leave-one-out Cross-validation (LOO-CV)\n",
"\n",
"The expected log pointwise predictive density (ELPD) quantifies how well a model is expected to predict new observations, averaged over data points. This quantity can be estimated in several ways, including cross-validation. In cross-validation, In cross-validation, the data are repeatedly partitioned into training and holdout sets, iteratively fitting the model with the former and evaluating the fit with the holdout data. When each data point is held out once, this is known as leave-one-out cross-validation (LOO-CV). Vehtari et al. (2016) introduced an efficient computation of LOO from MCMC samples (without the need for re-fitting the data). This approximation is based on importance sampling. The importance weights are stabilized using a method known as Pareto-smoothed importance sampling (PSIS), hence the full name PSIS-LOO-CV, but it is commonly referred to as LOO for brevity.\n",
"\n",
"### Model log-likelihood\n",
"\n",
"In order to compute LOO, ArviZ needs access to the model elemwise loglikelihood for every posterior sample. We can add it via {func}`~pymc.compute_log_likelihood`. Alternatively we can pass `idata_kwargs={\"log_likelihood\": True}` to {func}`~pymc.sample` to have it computed automatically at the end of sampling."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "4a48c1f8973542be9614ba6ce355c336",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Output()"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" rank \n",
" elpd \n",
" p \n",
" elpd_diff \n",
" weight \n",
" se \n",
" dse \n",
" warning \n",
" \n",
" \n",
" \n",
" \n",
" pooled \n",
" 0 \n",
" -30.57153 \n",
" 0.683161 \n",
" 0.00000 \n",
" 1.0 \n",
" 1.107647 \n",
" 0.000000 \n",
" False \n",
" \n",
" \n",
" hierarchical \n",
" 1 \n",
" -30.78649 \n",
" 1.149336 \n",
" 0.21496 \n",
" 0.0 \n",
" 1.068123 \n",
" 0.240133 \n",
" False \n",
" \n",
" \n",
"
\n",
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_compare(df_comp_loo);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The circles represent the ELPD values and the black error bars associated with them are the values of the standard deviation of the ELPDs. \n",
"\n",
"The value of the highest ELPD, i.e the best estimated model, is also indicated with a vertical dashed grey line to ease comparison with other ELPD values.\n",
"\n",
"For all models except the top-ranked one we also get a triangle indicating the value of the difference of ELPD between that model and the top model and a grey error bar indicating the standard error of the differences between the top-ranked ELPD and ELPD for each model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Interpretation\n",
"\n",
"Though we might expect the hierarchical model to outperform a complete pooling model, there is little to choose between the models in this case, given that both models gives very similar values of the expected log predictive density (ELPD). This is more clearly appreciated when we take into account the uncertainty (in terms of standard errors).\n",
"\n",
"## Reference\n",
"\n",
"[Gelman, A., Hwang, J., & Vehtari, A. (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24(6), 997–1016.](https://doi.org/10.1007/s11222-013-9416-2)\n",
"\n",
"[Vehtari, A, Gelman, A, Gabry, J. (2016). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing](http://link.springer.com/article/10.1007/s11222-016-9696-4)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Last updated: Sat Feb 14 2026\n",
"\n",
"Python implementation: CPython\n",
"Python version : 3.13.5\n",
"IPython version : 9.3.0\n",
"\n",
"xarray : 2025.6.1\n",
"pytensor: 2.36.1\n",
"\n",
"numpy: 2.2.6\n",
"arviz: 1.0.0rc0\n",
"pymc : 5.25.1+59.g4ba1d2f1c.dirty\n",
"\n",
"Watermark: 2.5.0\n",
"\n"
]
}
],
"source": [
"%load_ext watermark\n",
"\n",
"%watermark -n -u -v -iv -w -p xarray,pytensor"
]
}
],
"metadata": {
"hide_input": false,
"kernelspec": {
"display_name": "pymc",
"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": "3.13.5"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 4
}