Bayesian Data Analysis 3rd Edition - Overview

Bayesian Data Analysis, 3rd Edition

Summary

The definitive textbook on Bayesian statistics by Gelman, Carlin, Stern, Dunson, Vehtari, and Rubin (2013, updated 2025). Covers Bayesian inference from first principles through advanced computation and modeling. Uses R and Stan throughout.

Structure

Part I: Fundamentals of Bayesian Inference (Ch 1-5)

• Probability and Bayesian Inference — Bayes’ theorem, the three steps
• Single-Parameter Models — beta-binomial, conjugate priors
• Multiparameter Models — nuisance parameters, marginal posteriors
• Asymptotics and Frequentist Connections — normal approximation, BvM theorem
• Hierarchical Models — exchangeability, partial pooling, eight schools

Part II: Fundamentals of Bayesian Data Analysis (Ch 6-9)

• Model Checking — posterior predictive checks, Bayesian p-values
• Model Comparison — WAIC, LOO-CV, Bayes factors
• Data Collection Models — ignorability, surveys, experiments
• Decision Analysis — utility, loss functions, optimal decisions

Part III: Advanced Computation (Ch 10-13)

• Introduction to Bayesian Computation — simulation, importance sampling
• MCMC Basics — Gibbs sampler, Metropolis-Hastings, convergence
• Efficient MCMC — HMC, NUTS, Stan
• Approximation Methods — variational inference, Laplace, EP

Part IV: Regression Models (Ch 14-18)

• Bayesian Linear Regression — priors as regularization
• Hierarchical Linear Models — varying intercepts/slopes
• Generalized Linear Models — logistic, Poisson, GLMs
• Missing Data Models — multiple imputation

Part V: Nonlinear and Nonparametric Models (Ch 19-23)

• Nonparametric Models Overview — splines, GPs, mixtures, Dirichlet processes

Key Themes

1. Iterative model building: start simple, check, expand — formalized in Bayesian Workflow - Overview
2. Hierarchical modeling: the core of applied Bayesian statistics
3. Computation and software: Stan as the modern platform
4. Practical focus: real examples over pure theory

Authors

Andrew Gelman (Columbia), John Carlin (Melbourne), Hal Stern (UC Irvine), David Dunson (Duke), Aki Vehtari (Aalto), Donald Rubin (Harvard)

See Also (Cross-Domain)

• Bayesian Workflow - Overview — the companion paper codifying applied workflow practice
• Mostly Harmless Econometrics - Overview — the frequentist/econometric counterpart to BDA3
• Forking Paths and Bayesian Approaches — Bayesian rationale for addressing multiple comparisons