Bayesian Modeling with PyMC

From First Principles to Practice

Preface

You took a statistics course in grad school. You learned about \(p\)-values, confidence intervals, maximum likelihood, and maybe even heard the word “Bayesian” in a lecture or two. Then you spent a decade building things — writing Python, wrangling data, shipping models. The statistics got rusty. The Bayesian part never quite stuck.

This book fixes that. It teaches Bayesian modeling with PyMC from first principles, assuming you know Python and have a faded memory of statistics. Every concept is introduced through code you can run, not notation you have to decode. Every model is built step by step, with explanations of why each choice is made — not just what buttons to push.

Who this book is for. Junior developers building data pipelines, beginning data analysts who want to move beyond point estimates, and fresh (or not-so-fresh) graduate students who need a clean, modern introduction to Bayesian methods. You should be comfortable with Python, NumPy, and pandas. Prior experience with PyMC is not assumed.

What you will learn:

• How to think about probability as a measure of uncertainty, not just a long-run frequency
• How to build, fit, and diagnose Bayesian models in PyMC
• How to use hierarchical models to borrow strength across groups
• How to check whether your model is any good (prior predictive checks, posterior predictive checks, model comparison)
• How to apply Gaussian processes, nonparametric Bayesian methods, and causal inference in a Bayesian framework
• How to solve real business problems (A/B testing, marketing mix, demand forecasting) with Bayesian decision making

What this book is based on. The content draws on over 40 talks from the PyMC and PyData communities, given by the creators and core developers of PyMC (Thomas Wiecki, Chris Fonnesbeck, Austin Rochford, and many others). We distilled their collective wisdom into a structured tutorial that builds from basics to advanced methods.

How to Read This Book

Each chapter follows a consistent pattern:

1. The idea — what problem this method solves, in plain language
2. The math — just enough theory to understand what the code does and why
3. The code — complete PyMC models you can run, with every line explained
4. The diagnostics — how to check whether the model worked
5. The interpretation — what the results mean and how to communicate them

Environment

All code targets PyMC 5.x with ArviZ for diagnostics.

python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

import pymc as pm
import arviz as az
import numpy as np
import matplotlib.pyplot as plt

print(f"PyMC:    {pm.__version__}")
print(f"ArviZ:   {az.__version__}")
print(f"NumPy:   {np.__version__}")

PyMC:    5.25.1
ArviZ:   0.23.4
NumPy:   2.2.6