Bayesian Workflow
Routing Summary
This folder covers the iterative Bayesian modeling cycle. Three sources: the 2026 textbook Bayesian Workflow (Gelman, Vehtari & McElreath) in 79 notes across six sub-folders, the 2020 arXiv paper it expands (7 notes, kept and cross-linked), and Simulation-Based Calibration (Talts et al. 2018, 6 notes). Contains 92 notes.
Start here for the textbook: Bayesian Workflow Book - Overview — the routing index for all 79 book notes.
- Need the master workflow diagram (Figure 2.1)? → From Inference to Data Analysis to Workflow
- Need to specify a model or a prior? → Building Models
- Need to check or compare fitted models? → Evaluating and Comparing
- Need diagnostics, failure modes, or approximate inference? → Computational Workflow
- Need a worked analysis of a real problem? → Case Studies (16 of them, routed by symptom)
- Need the non-Bayesian translation or a BDA3 reading guide? → Appendices
- Need foundations: why Bayes, the four scenarios, Stan setup? → Foundations
From the 2020 paper (kept, each with an
expanded_bypointer):
- Need the paper’s compact workflow overview / Figure 1? → Bayesian Workflow - Overview
- Need the paper on prior predictive checking or model building? → Choosing and Building Models
Simulation-Based Calibration (Talts et al. 2018) — theory, complementary to the book:
- Need the SBC method / fake-data validation at a glance? → Simulation-Based Calibration - Overview
- Need the SBC foundational identity (prior = data-averaged posterior)? → Data-Averaged Posterior Self-Consistency
- Need the rank statistic + uniformity theorem? → Rank Statistics and Uniformity
- Need the step-by-step SBC recipe (Algorithm 1 & 2)? → The SBC Algorithm
- Need to read SBC histogram shapes (∪/∩/sloped) or handle autocorrelation? → Interpreting SBC Histograms
- Need worked SBC examples (HMC/ADVI/INLA, 8-schools)? → SBC Case Studies
- Need SBC in the broader workflow context? → SBC in the Workflow (book) or Fitting and Validating Computation (paper)
- Need to debug divergences or multimodality? → Failure Modes and Steps Forward (book) or Computational Troubleshooting (paper)
- Need version control for models? → Statistical Modeling as Software Development (book) or Modeling as Software Development (paper)
Sub-folders (2026 textbook, 79 notes)
| Sub-folder | Notes | Covers |
|---|---|---|
| Foundations | 8 | Why Bayes, varieties of Bayesian theory, the master workflow diagram, four modeling scenarios, Stan setup, two introductory examples (Ch. 1–4) |
| Building Models | 19 | Model specification, every prior-choice rule, prior predictive checking, simulation as a modeling tool, poststratification, causal inference, decision (Ch. 5–7) |
| Evaluating and Comparing | 16 | Posterior predictive checking, PSIS-LOO and Pareto , influence and sensitivity, model selection, stacking, model expansion, the replication crisis (Ch. 8–10) |
| Computational Workflow | 16 | The typical set, /ESS/MCSE, fail-fast development, the catalogue of failure modes, approximate inference, Pathfinder, modeling as software development (Ch. 11–13, 15) |
| Simulation-Based Calibration | 1 | SBC as an integrated workflow step, the metric (Ch. 14) |
| Case Studies | 16 | Sixteen complete analyses, each with model spec, what went wrong, and the lesson — routed by symptom (Ch. 16–31) |
| Appendices | 2 | The non-Bayesian translation of the whole workflow; a chapter-by-chapter BDA3 reading guide (App. A–B) |
| Bayesian Workflow Book - Overview | 1 | The routing index for all 79 book notes (lives at this folder’s root) |
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| The 2026 textbook, 31 chapters + 2 appendices | Bayesian Workflow Book - Overview | overview | Bayesian Workflow - Overview | Routing index for all 79 book notes; the case-study symptom table |
| Master workflow diagram (Figure 2.1) | From Inference to Data Analysis to Workflow | concept | Why Bayes - Benefits, Costs, and Borders | Inference ⊂ data analysis ⊂ workflow, transcribed as mermaid |
| Full workflow vs mere Bayesian inference, Figure 1 | Bayesian Workflow - Overview | overview | Probability and Bayesian Inference, MCMC Basics, Hierarchical Models | Workflow = iterative cycle, not just fitting |
| Model selection, modular construction, prior predictive | Choosing and Building Models | concept | Bayesian Workflow - Overview, Hierarchical Models, Probability and Bayesian Inference | Build models modularly, check priors first |
| Warmup, convergence, fake-data simulation, SBC | Fitting and Validating Computation | concept | Choosing and Building Models, MCMC Basics, Efficient MCMC, Bayesian Workflow - Overview | SBC validates the full inference pipeline |
| Folk theorem, reparameterization, multimodality | Computational Troubleshooting | concept | Fitting and Validating Computation, MCMC Basics, Efficient MCMC, Hierarchical Models | Computational problems often signal model problems |
| Posterior predictive checks, cross-validation, prior influence | Evaluating Fitted Models | concept | Fitting and Validating Computation, Computational Troubleshooting, Hierarchical Models, Bayesian Workflow - Overview | Evaluate models against data and domain knowledge |
| Model modification, topology of models, stacking | Iterative Model Improvement | concept | Evaluating Fitted Models, Choosing and Building Models, Hierarchical Models, Bayesian Workflow - Overview | Expand or modify models based on evaluation |
| Version control, testing, reproducibility | Modeling as Software Development | concept | Bayesian Workflow - Overview, Fitting and Validating Computation, Choosing and Building Models, Evaluating Fitted Models | Treat model code like software |
| SBC method, validates correct posterior sampling, generalizes Cook-Gelman-Rubin (2006) | Simulation-Based Calibration - Overview | overview | Data-Averaged Posterior Self-Consistency, Bayesian Workflow - Overview | SBC checks computation, complements PPCs |
| Prior = average of exact posteriors over joint-distribution data (Eq. 1) | Data-Averaged Posterior Self-Consistency | theorem | — | Data-averaged posterior equals the prior |
| Rank of prior draw in posterior sample ~ discrete Uniform[0,L] (Theorem 1) | Rank Statistics and Uniformity | theorem | Data-Averaged Posterior Self-Consistency | Ranks uniform iff sampling is exact & independent |
| SBC procedure: sample θ | The SBC Algorithm | concept | Rank Statistics and Uniformity, Data-Averaged Posterior Self-Consistency | N parallel fits, L draws → rank histogram |
| Histogram shapes: ∪=under-dispersed, ∩=over-dispersed, sloped=biased; autocorrelation/thinning; ECDF | Interpreting SBC Histograms | concept | The SBC Algorithm, Rank Statistics and Uniformity | Deviation shape diagnoses the failure mode |
| Worked SBC experiments: misspecified prior, centered 8-schools HMC bias, ADVI, INLA spatial | SBC Case Studies | example | The SBC Algorithm, Interpreting SBC Histograms | SBC catches distinct real failure modes |
Notes
2026 textbook (79 notes — see the sub-folder indexes above):
- Bayesian Workflow Book - Overview — CONTAINS: the routing table for all 79 notes, the five-part structure, the sixteen-case-study symptom index, and the mapping from each 2020-paper note to its book expansion
2020 arXiv paper (kept and cross-linked):
- Bayesian Workflow - Overview — CONTAINS: Full workflow diagram (Figure 1), workflow vs inference distinction, iterative cycle overview
- Choosing and Building Models — CONTAINS: Initial model selection, modular construction, prior predictive checking, domain expertise integration
- Fitting and Validating Computation — CONTAINS: MCMC warmup, convergence checks, fake-data simulation, simulation-based calibration (SBC)
- Computational Troubleshooting — CONTAINS: Folk theorem of statistical computing, reparameterization strategies, multimodality diagnosis
- Evaluating Fitted Models — CONTAINS: Posterior predictive checks, cross-validation, sensitivity to priors, residual analysis
- Iterative Model Improvement — CONTAINS: Model expansion, topology of model space, Bayesian stacking, when to stop iterating
- Modeling as Software Development — CONTAINS: Version control for models, unit testing, reproducibility practices, documentation
- Simulation-Based Calibration - Overview — CONTAINS: What SBC validates (correct posterior sampling), naive single-dataset check counterexample, relation to Geweke (2004) and Cook-Gelman-Rubin (2006), complement to posterior predictive checks, place in the workflow
- Data-Averaged Posterior Self-Consistency — CONTAINS: Eq. 1 self-consistency identity (prior = data-averaged posterior), full statement + notation + proof sketch, data-averaged posterior definition
- Rank Statistics and Uniformity — CONTAINS: Rank statistic construction (Eq. 4.1), Theorem 1 uniformity statement + conditions (independence, exact sampling), Appendix B proof sketch, why ranks beat CDF values
- The SBC Algorithm — CONTAINS: Algorithm 1 (ideal) and Algorithm 2 (thinned MCMC) step by step, choice of N and L, 99% Binomial confidence band, re-binning, effective-sample-size thinning
- Interpreting SBC Histograms — CONTAINS: Uniform/∪/∩/sloped shape catalogue and meanings, autocorrelation boundary spikes + thinning correction (N_eff, CLT), ECDF and ECDF-difference for small deviations
- SBC Case Studies — CONTAINS: Misspecified-prior ∪-shape (6.1), centered 8-schools HMC bias + non-centered autocorrelation (6.2), ADVI gross slope bias (6.3), INLA subtle spatial bias via ECDF (6.4), Stan Listings 1-4
Sources
- Gelman Vehtari McElreath 2026 - Bayesian Workflow (book) — Gelman, Vehtari & McElreath (2026), Bayesian Workflow, 550 pp. — the full-length textbook expansion of the 2020 paper
- BayesWorkflow — Gelman et al. (2020), arXiv:2011.01808
- 1804.06788-Talts-SBC — Talts, Betancourt, Simpson, Vehtari & Gelman (2018), “Validating Bayesian Inference Algorithms with Simulation-Based Calibration”, arXiv:1804.06788 (shares authors with the Bayesian Workflow paper and BDA3)