Python Bayesian Analysis

This book explains the main concepts of Bayesian statistics from a practical and programming perspective, and demonstrates how to build, check, and extend probabilistic models using the Python probabilistic programming library PyMC3. It opens with “probabilistic thinking,” first explaining the core ideas of Bayesian inference—priors, likelihoods, posteriors, and credible intervals—in an intuitive way before moving on to the concrete syntax of probabilistic programming. It then discusses multi-parameter and hierarchical models in turn, introducing how linear regression can be used to understand and predict data and how logistic regression can accomplish classification tasks; a separate chapter on model comparison follows, explaining how to evaluate and select models under uncertainty using methods such as information criteria; the book then moves on to more advanced topics such as mixture models and Gaussian processes, addressing heterogeneous populations, clustering structures, and nonlinear relationships. The book uses manually constructed data and some real data to demonstrate the modeling workflow, emphasizing “code that runs” and interpretation of results rather than mathematical derivations. After reading, readers should be able to independently implement, diagnose, and modify Bayesian models and assess model performance using posterior predictive checks. The book requires no prior statistical knowledge but does require readers to have Python programming experience.