PyMC Example Gallery#

A collection of runnable Jupyter notebooks showing how to solve real modeling problems with PyMC, from simple regression to advanced Bayesian workflows.

Introductory#

General Overview

Introductory Overview of PyMC

Simple Linear Regression

GLM: Linear regression

General API quickstart

General API quickstart

Library Fundamentals#

Distribution Dimensionality

Distribution Dimensionality

PyMC and PyTensor

PyMC and PyTensor

Using Data Containers

Using Data Containers

How to#

Prior and Posterior Predictive Checks

Prior and Posterior Predictive Checks

Model Comparison

Model comparison

LKJ Cholesky Covariance Priors for Multivariate Normal Models

LKJ Cholesky Covariance Priors for Multivariate Normal Models

Bayesian Missing Data Imputation

Bayesian Missing Data Imputation

Using a “black box” likelihood function

Using a “black box” likelihood function

Bayesian copula estimation: Describing correlated joint distributions

Bayesian copula estimation: Describing correlated joint distributions

How to debug a model

How to debug a model

Bayesian Hypothesis Testing - an introduction

Bayesian Hypothesis Testing - an introduction

Automatic marginalization of discrete variables

Automatic marginalization of discrete variables

Using ModelBuilder class for deploying PyMC models

Using ModelBuilder class for deploying PyMC models

Updating Priors

Updating Priors

How to wrap a JAX function for use in PyMC

How to wrap a JAX function for use in PyMC

Generalized Linear Models#

Binomial regression

Binomial regression

Discrete Choice and Random Utility Models

Discrete Choice and Random Utility Models

Hierarchical Binomial Model: Rat Tumor Example

Hierarchical Binomial Model: Rat Tumor Example

GLM-missing-values-in-covariates

GLM-missing-values-in-covariates

GLM: Model Selection

GLM: Model Selection

GLM: Negative Binomial Regression

GLM: Negative Binomial Regression

GLM-ordinal-features

GLM-ordinal-features

Regression Models with Ordered Categorical Outcomes

Regression Models with Ordered Categorical Outcomes

Out-Of-Sample Predictions

Out-Of-Sample Predictions

GLM: Poisson Regression

GLM: Poisson Regression

Heteroscedastic Bayesian Robust Regression

Heteroscedastic Bayesian Robust Regression

GLM: Robust Regression using Custom Likelihood for Outlier Classification

GLM: Robust Regression using Custom Likelihood for Outlier Classification

GLM: Robust Linear Regression

GLM: Robust Linear Regression

Rolling Regression

Rolling Regression

Bayesian regression with truncated or censored data

Bayesian regression with truncated or censored data

A Primer on Bayesian Methods for Multilevel Modeling

A Primer on Bayesian Methods for Multilevel Modeling

Case Studies#

Bayesian Estimation Supersedes the T-Test

Bayesian Estimation Supersedes the T-Test

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics

Confirmatory Factor Analysis and Structural Equation Models in Psychometrics

Generalized Extreme Value Distribution

Generalized Extreme Value Distribution

Bayesian Workflow with SEMs

Bayesian Workflow with SEMs

The Bayesian Workflow: COVID-19 Outbreak Modeling

The Bayesian Workflow: COVID-19 Outbreak Modeling

Estimating parameters of a distribution from awkwardly binned data

Estimating parameters of a distribution from awkwardly binned data

Factor analysis

Factor analysis

Hierarchical Partial Pooling

Hierarchical Partial Pooling

NBA Foul Analysis with Item Response Theory

NBA Foul Analysis with Item Response Theory

Estimating species distributions with occupancy models

Estimating species distributions with occupancy models

Probabilistic Matrix Factorization for Making Personalized Recommendations

Probabilistic Matrix Factorization for Making Personalized Recommendations

Model building and expansion for golf putting

Model building and expansion for golf putting

Fitting a Reinforcement Learning Model to Behavioral Data with PyMC

Fitting a Reinforcement Learning Model to Behavioral Data with PyMC

Reliability Statistics and Predictive Calibration

Reliability Statistics and Predictive Calibration

A Hierarchical model for Rugby prediction

A Hierarchical model for Rugby prediction

Forecasting Hurricane Trajectories with State Space Models

Forecasting Hurricane Trajectories with State Space Models

Topological posterior predictive checks with PyMC

Topological posterior predictive checks with PyMC

Causal Inference#

Simpson’s paradox

Simpson’s paradox

Assurance Planning via Simulation

Assurance Planning via Simulation

Introduction to Bayesian A/B Testing

Introduction to Bayesian A/B Testing

Bayesian Non-parametric Causal Inference

Bayesian Non-parametric Causal Inference

Difference in differences

Difference in differences

Counterfactual inference: calculating excess deaths due to COVID-19

Counterfactual inference: calculating excess deaths due to COVID-19

Interrupted time series analysis

Interrupted time series analysis

Interventional distributions and graph mutation with the do-operator

Interventional distributions and graph mutation with the do-operator

Interventional what-if analysis using the PyMC do-operator

Interventional what-if analysis using the PyMC do-operator

Bayesian mediation analysis

Bayesian mediation analysis

Bayesian moderation analysis

Bayesian moderation analysis

Multiple Experiments and Bayesian Meta-analysis

Multiple Experiments and Bayesian Meta-analysis

Regression discontinuity design analysis

Regression discontinuity design analysis

Sensitivity Analysis for Unmeasured Confounding

Sensitivity Analysis for Unmeasured Confounding

Gaussian Processes#

Baby Births Modelling with HSGPs

Baby Births Modelling with HSGPs

Heteroskedastic Gaussian Processes

Heteroskedastic Gaussian Processes

Kronecker Structured Covariances

Kronecker Structured Covariances

Gaussian Processes: Latent Variable Implementation

Gaussian Processes: Latent Variable Implementation

Marginal Likelihood Implementation

Marginal Likelihood Implementation

Gaussian Process for CO2 at Mauna Loa

Gaussian Process for CO2 at Mauna Loa

Example: Mauna Loa CO_2 continued

Example: Mauna Loa CO_2 continued

Mean and Covariance Functions

Mean and Covariance Functions

Sparse Approximations

Sparse Approximations

Student-t Process

Student-t Process

Gaussian Process (GP) smoothing

Gaussian Process (GP) smoothing

Gaussian Processes: HSGP Advanced Usage

Gaussian Processes: HSGP Advanced Usage

Gaussian Processes: HSGP Reference & First Steps

Gaussian Processes: HSGP Reference & First Steps

Multi-output Gaussian Processes: Coregionalization models using Hamadard product

Multi-output Gaussian Processes: Coregionalization models using Hamadard product

Gaussian Processes using numpy kernel

Gaussian Processes using numpy kernel

Modeling spatial point patterns with a marked log-Gaussian Cox process

Modeling spatial point patterns with a marked log-Gaussian Cox process

Time Series#

Analysis of An AR(1) Model in PyMC

Analysis of An AR(1) Model in PyMC

Air passengers - Prophet-like model

Air passengers - Prophet-like model

Inferring parameters of SDEs using a Euler-Maruyama scheme

Inferring parameters of SDEs using a Euler-Maruyama scheme

Forecasting with Structural AR Timeseries

Forecasting with Structural AR Timeseries

Multivariate Gaussian Random Walk

Multivariate Gaussian Random Walk

Time Series Models Derived From a Generative Graph

Time Series Models Derived From a Generative Graph

Bayesian Vector Autoregressive Models

Bayesian Vector Autoregressive Models

Longitudinal Models of Change

Longitudinal Models of Change

Stochastic Volatility model

Stochastic Volatility model

Spatial Analysis#

Conditional Autoregressive (CAR) Models for Spatial Data

Conditional Autoregressive (CAR) Models for Spatial Data

The prevalence of malaria in the Gambia

The prevalence of malaria in the Gambia

The Besag-York-Mollie Model for Spatial Data

The Besag-York-Mollie Model for Spatial Data

Diagnostics and Model Criticism#

Bayes Factors and Marginal Likelihood

Bayes Factors and Marginal Likelihood

Diagnosing Biased Inference with Divergences

Diagnosing Biased Inference with Divergences

Model Averaging

Model Averaging

Sampler Statistics

Sampler Statistics

Bayesian Additive Regression Trees#

Categorical regression

Categorical regression

Modeling Heteroscedasticity with BART

Modeling Heteroscedasticity with BART

Bayesian Additive Regression Trees: Introduction

Bayesian Additive Regression Trees: Introduction

Quantile Regression with BART

Quantile Regression with BART

Mixture Models#

Dependent density regression

Dependent density regression

Dirichlet mixtures of multinomials

Dirichlet mixtures of multinomials

Hidden Markov Models in PyMC: marginalize and recover a DiscreteMarkovChain

Hidden Markov Models in PyMC: marginalize and recover a DiscreteMarkovChain

Dirichlet process mixtures for density estimation

Dirichlet process mixtures for density estimation

Gaussian Mixture Model

Gaussian Mixture Model

Marginalized Gaussian Mixture Model

Marginalized Gaussian Mixture Model

Survival Analysis#

Bayesian Parametric Survival Analysis

Bayesian Parametric Survival Analysis

Censored Data Models

Censored Data Models

Frailty and Survival Regression Models

Frailty and Survival Regression Models

Bayesian Survival Analysis

Bayesian Survival Analysis

Reparameterizing the Weibull Accelerated Failure Time Model

Reparameterizing the Weibull Accelerated Failure Time Model

ODE models#

GSoC 2019: Introduction of pymc3.ode API

GSoC 2019: Introduction of pymc3.ode API

pymc3.ode: Shapes and benchmarking

pymc3.ode: Shapes and benchmarking

ODE Lotka-Volterra With Bayesian Inference in Multiple Ways

ODE Lotka-Volterra With Bayesian Inference in Multiple Ways

Lotka-Volterra with manual gradients

Lotka-Volterra with manual gradients

MCMC#

DEMetropolis and DEMetropolis(Z) Algorithm Comparisons

DEMetropolis and DEMetropolis(Z) Algorithm Comparisons

DEMetropolis(Z) Sampler Tuning

DEMetropolis(Z) Sampler Tuning

Approximate Bayesian Computation

Approximate Bayesian Computation

Sequential Monte Carlo

Sequential Monte Carlo

Faster Sampling with JAX and Numba

Faster Sampling with JAX and Numba

Lasso regression with block updating

Lasso regression with block updating

Compound Steps in Sampling

Compound Steps in Sampling

Using a custom step method for sampling from locally conjugate posterior distributions

Using a custom step method for sampling from locally conjugate posterior distributions

Variational Inference#

GLM: Mini-batch ADVI on hierarchical regression model

GLM: Mini-batch ADVI on hierarchical regression model

Variational Inference: Bayesian Neural Networks

Variational Inference: Bayesian Neural Networks

Empirical Approximation overview

Empirical Approximation overview

Pathfinder Variational Inference

Pathfinder Variational Inference

Introduction to Variational Inference with PyMC

Introduction to Variational Inference with PyMC

Statistical Rethinking Lectures#

The Garden of Forking Data

The Garden of Forking Data

Geocentric Models

Geocentric Models

Categories and Curves

Categories and Curves

Elemental Confounds

Elemental Confounds

Good & Bad Controls

Good & Bad Controls

Fitting Over & Under

Fitting Over & Under

Markov Chain Monte Carlo

Markov Chain Monte Carlo

Modeling Events

Modeling Events

Counts and Hidden Confounds

Counts and Hidden Confounds

Ordered Categories

Ordered Categories

Multilevel Models

Multilevel Models

Multilevel Adventures

Multilevel Adventures

Correlated Features

Correlated Features

Social Networks

Social Networks

Gaussian Processes

Gaussian Processes

Measurement and Misclassification

Measurement and Misclassification

Generalized Linear Madness

Generalized Linear Madness