Bayesian Workflow Book - Overview

Bayesian Workflow (Gelman, Vehtari & McElreath, 2026) — Overview

Summary

The full-length textbook expansion of the 2020 arXiv paper [[Bayesian Workflow - Overview|Bayesian Workflow]]. 31 chapters plus two appendices, in five parts: foundations, building models, evaluating and comparing, computation, and sixteen worked case studies. This vault holds 79 notes covering all parts in depth — every prior-choice rule, diagnostic threshold, failure mode, and Stan snippet from Parts 1–3, plus one note per case study recording the model specification, what went wrong, and the lesson.

Overview

The book’s thesis is that Bayesian inference is only one step in Bayesian data analysis, and Bayesian data analysis is only one step in a workflow that includes model building, computation, checking, expansion, comparison, and decision. Most of what practitioners actually do is not covered by inference theory, and the book’s project is to make that tacit knowledge explicit.

The single most important routing artifact is the master workflow diagram, Figure 2.1, transcribed as a mermaid graph in From Inference to Data Analysis to Workflow. Read that first if you want to know where any particular technique sits.

Routing Table

Where to go for what

If you need…	Go to
The master workflow diagram	From Inference to Data Analysis to Workflow
Why Bayes, and when it isn’t worth it	Why Bayes - Benefits, Costs, and Borders
The taxonomy organizing the whole book	Four Modeling Scenarios
One problem carried end to end	Multiple-Choice Exam - A Full Workflow Walkthrough
Where to start: the first model to write down	Choosing an Initial Model, Generative and Partially Generative Models
How to pick and specify a prior	Prior Distributions, Constructing Priors for Effect Sizes, Joint Priors and Covariance Matrices
Checking a model before seeing data	Prior Predictive Checking
Testing a model and its code on fake data	Designing Simulated-Data Experiments
Checking a model after fitting	Posterior Predictive Checking, Cross Validation Checking
Choosing between models	Model Selection Using Predictive Performance, Stacking and Predictive Model Averaging
Chains that won’t mix	What to Do About Convergence Problems, Failure Modes and Steps Forward
Validating that your Stan program is correct	SBC in the Workflow, Simulation-Based Calibration Checking in Model Development Workflow
Keeping the modeling loop fast	Fit Fast, Fail Fast
A fast approximation to fit-and-fail-fast	Variational Inference and Pathfinder, Approximate Algorithms and Approximate Models
Causal effects and generalization	Causal Inference as Generalization, Poststratification
What a fitted model does and does not tell you scientifically	Statistical and Scientific Inference
A non-Bayesian translation of everything above	Statistical and Computational Workflow for Bayesians and Non-Bayesians
What to read in BDA3 and what to skip	How to Get the Most Out of Bayesian Data Analysis

Structure

Part	Chapters	Folder	Notes
Part 1 — Foundations	1–4	Foundations	8
Part 2 — Building models	5–7	Building Models	19
Part 3a — Evaluating and comparing	8–10	Evaluating and Comparing	16
Part 3b — Computation	11–13, 15	Computational Workflow	16
Part 3c — SBC	14	Simulation-Based Calibration	1
Part 4 — Case studies	16–31	Case Studies	16
Appendices	A–B	Appendices	2
This overview	—	(folder root)	1
Total			79

The Sixteen Case Studies

Each case study note records the model specification, what went wrong, and the transferable lesson.

Ch.	Case study	Central lesson
16	Coding a Series of Models - Movie Ratings	Build a model as a sequence, not a single artifact
17	Prior Specification for Regression Models - Sleep Study	Priors as part of the model, not a formality
18	Predictive Model Checking and Comparison - Clinical Trial	Predictive checks drive comparison
19	Building Up to a Hierarchical Model - Coronavirus Testing	Hierarchy earned incrementally
20	Using a Fitted Model for Decision Analysis - Classification Competition	Inference is not the endpoint
21	Posterior Predictive Checking - Stochastic Learning in Dogs	What a graphical check actually reveals
22	Incremental Development and Testing - Black Cat Adoptions	Test each component as you add it
23	Debugging a Model - World Cup Football	Finding a bug in a model you believe
24	LOO Model Checking and Comparison - Roaches	Pareto $\hat{k}$, p_loo, and what they mean
25	Model Building and Expansion - Golf Putting	Physical reasoning beats flexible curves
26	Model Building with Latent Variables - Animal Movement	Latent structure with real interpretation
27	Model Building - Time-Series Decomposition for Birthdays	Additive decomposition, GP approximation, and two honest failures
28	Models for Regression Coefficients - Student Grades	With a good prior, you don’t need variable selection
29	Sampling Problems with Latent Variables - No Vehicles in the Park	Non-centered is not always right
30	Challenge of Multimodality - Differential Equation for Planetary Motion	Multimodality reparameterization cannot fix
31	Simulation-Based Calibration Checking in Model Development Workflow	SBC as a debugging subroutine

Relation to the 2020 Paper

The seven notes derived from the 2020 arXiv paper remain in this folder, each carrying an expanded_by frontmatter field and a callout pointing to the book’s expanded treatment:

• Bayesian Workflow - Overview → From Inference to Data Analysis to Workflow
• Choosing and Building Models → Building Models
• Evaluating Fitted Models → Evaluating and Comparing
• Computational Troubleshooting → Failure Modes and Steps Forward
• Fitting and Validating Computation → Computational Workflow
• Iterative Model Improvement → Model Expansion - Predictive Consistency and Coherence
• Modeling as Software Development → Statistical Modeling as Software Development

The six notes from Talts et al. (2018) on SBC are complementary rather than superseded: they carry the theory (the data-averaged posterior identity, the uniformity theorem, histogram interpretation), while SBC in the Workflow and Simulation-Based Calibration Checking in Model Development Workflow carry the book’s practical integration.

See Also

• Bayesian Workflow - Overview — the 2020 paper this book expands
• Simulation-Based Calibration - Overview — the Talts et al. theory notes
• _Index — the folder index