Bayesian Workflow

Andrew Gelman is a professor of statistics and political science at Columbia UniversityAki Vehtari is a professor of computer science at Aalto UniversityRichard McElreath is the director of the Max Planck Institute for Evolutionary AnthropologyDaniel Simpson is a machine learning engineer at dottxtCharles Margossian is an assistant professor of statistics at the University of British ColumbiaYuling Yao is an assistant professor of statistics at the University of TexasLauren Kennedy is a senior lecturer in mathematical science at the University of AdelaideJonah Gabry is an applied statistics researcher at Columbia UniversityPaul-Christian Bürkner is a professor of statistics at TU Dortmund UniversityMartin Modrák is a researcher in bioinformatics at Charles UniversityVianey Leos Barajas is an assistant professor of statistical sciences at the University of Toronto

“This is an important book…The text magnificently achieves its aim of leading the reader through this workflow, which involves iterative model building, model checking, validation and troubleshooting of computational problems, as well as model understanding and model comparison. These aspects of the workflow are considered in the context of several, diverse examples…Despite its length, the book is beautifully structured, as a series of 31 chapters, each a relatively short and carefully crafted essay on some aspect of the Bayesian workflow. Each chapter includes a set of quite open-ended exercises, so the text would serve as an excellent basis for an extensive advanced course on contemporary applied Bayesian data analysis…The book is ‘not a checklist, not a cookbook’ but fully achieves its aim of presenting a flexible framework for understanding and analysing challenges in Bayesian statistical modelling and decision-making under uncertainty…The authors have produced a tour-de-force. By elegantly systematizing the processes of Bayesian model development and criticism, they have provided a work which provides a road map for improved applied Bayesian data analysis. It is certain to influence developments in applied statistical analysis, as well as inspire future innovations in Bayesian theory, methodology and computational software.”~Alastair Young, Imperial College, UK, published in International Statistical Review, July 2026“An outstanding, protocol-driven guide for Bayesian data analysis, Bayesian Workflow by Gelman, Vehtari, McElreath and co-authors delivers a practical and comprehensive framework for iterative modeling, emphasizing simulation, diagnostic checks, and rigorous empirical validation, and with a long and impressive list of case studies. By treating data analysis as a structured, verifiable workflow, it provides an indispensable toolkit for diagnosing model failures, refining priors, and building reliable data analysis systems for reproducible conclusions, useful for beginning and veteran data analysts alike.”~Bin Yu, CDSS Chancellor’s Distinguished Professor of Statistics, Electrical Engineering and Computer Sciences, and Center for Computational Biology, UC Berkeley, USA“This is not a typical methods textbook, but instead it guides the reader through the whole process of fitting, critiquing and adapting statistical models to real-world problems. It is full of the accumulated wisdom of skilled practitioners, teaching through demonstration rather than theory, with both basic and highly sophisticated examples. I strongly recommend this book to statisticians who really want to understand what they can learn from their data.”~Sir David Spiegelhalter, University of Cambridge, UK"A bravura performance...Gelman, Vehtari, McElreath and friends develop in detail a practical Bayesian data analysis workflow, from acquisition to final report, including full computational guidance.”~Brad Efron, Stanford University, USA"This original, thought-provoking, and transformative book is much much more than an implementation manual for Bayesian Data Analysis, even though it shares almost the same perspective. (The first sentence of the book states that the authors' "conceptions of statistical practice, and of Bayesian statistics, have changed over the years".) By providing a modus vivendi for undertaking Bayesian modelling from scratch in realistic settings where models are not magicked out of the blue, the authors explicit and rationalise the many steps required by such a bottom-up modelling protocol ("not a checklist, not a cookbook", and not a flowchart!) in real situations. The contents read very well and very smoothly, with a seamless conjunction of intuition, modelling advices, computational details, and comparison tools. While unsurprisingly Bayesian, the perspective adopted therein remains both open and inclusive, with a welcome humility about the limitations and challenges of Bayesian workflows. This book should thus appeal to and profit a wide variety of readers, as providing guidance through an extensive collection of highly detailed examples, with shared code and exercises.”~Christian P. Robert, Université Paris Dauphine PSL, Paris, France“Some statistics books show you how to beat an egg, others are recipe books: if this, then that style. This book teaches you how to cook. Written by authors who established so much of how we do Bayesian statistics, this new book is an indispensable guide for analyzing data in a trustworthy way. It walks you through the actual steps involved in building models to explore and understand datasets. Part 4 is particularly excellent – the authors provide many end-to-end case studies that will be useful for both practitioners and students. It highlights the value of their workflow-based approach. Filled with chatty asides, the book introduces the Bayesian workflow to a broad audience. It embraces the frustrations and complexities of actually doing Bayesian statistics and provides specific guidance throughout. Each chapter contains exercises and it could be the basis of an upper-year undergraduate course, or a first-year grad course, in applied statistics. It will be used for many years to come.”~Rohan Alexander, University of Toronto, Canada“What makes Bayesian Workflow so exceptional is how it seamlessly pairs profound ideas about modeling with the adoption of modern computational practice. By centering the messy, iterative process of modeling through real-world case studies, the authors reject rigid cookbooks and checklists in favor of building deep situational awareness. Because the ideas are so clearly articulated and deeply applied, this book serves as an invaluable pedagogical resource. With its practical exercises, individual chapters or the text as a whole can easily be integrated into upper-level undergraduate or graduate courses, while also remaining accessible for self-guided readers. It is an indispensable read for anyone with foundational knowledge in Bayesian methods, regardless of whether they are applied practitioners, software developers, or methodologists.”~Mine Doğucu, Senior Lecturer on Statistics, Harvard University, USA

• Part 1: From Bayesian inference to Bayesian workflow. 1 Bayesian theory and Bayesian practice. 2 Statistical modeling and workflow. 3 Computational tools. 4 Introduction to workflow: Modeling performance on a multiple choice exam. Part 2: Statistical workflow. 5 Building statistical models. 6 Using simulations to capture uncertainty. 7 Prediction, generalization, and causal inference/ 8 Visualizing and checking fitted models. 9 Comparing and improving models. 10 Statistical inference and scientific inference. Part 3: Computational workflow. 11 Fitting statistical models. 12 Diagnosing and fixing problems with fitting. 13 Approximate algorithms and approximate models. 14 Simulation-based calibration checking. 15 Statistical modeling as software development. Part 4: Case studies. 16 Coding a series of models: Simulated data of movie ratings. 17 Prior specification for regression models: Reanalysis of a sleep study.18 Predictive model checking and comparison: Clinical trial. 19 Building up to a hierarchical model: Coronavirus testing. 20 Using a fitted model for decision analysis: Mixture model for time series competition. 21 Posterior predictive checking: Stochastic learning in dogs. 22 Incremental development and testing: Black cat adoptions. 23 Debugging a model: World Cup football. 24 Leave-one-out cross validation model checking and comparison: Roaches. 25 Model building and expansion: Golf putting. 26 Model building with latent variables: Markov models for animal movement. 27 Model building: Time-series decomposition for birthdays. 28 Models for regression coefficients and variable selection: Student grades. 29 Funnel problem with latent variables: No vehicles in the park. 30 Computational challenge of multimodality: Differential equation for planetary motion. 31 Simulation-based calibration checking in model development workflow.