Bayesian Statistics
Routing Summary
This folder covers comprehensive Bayesian statistics from BDA3, Statistical Rethinking, the 2026 Bayesian Workflow textbook (Gelman, Vehtari & McElreath), the 2020 Bayesian Workflow paper, simulation-based calibration (SBC), synthetic likelihood, and PyMC tutorials. Contains 201 notes across 8 sub-topics.
- Need inference basics (Bayes’ theorem, conjugate priors, hierarchical)? → Inference Fundamentals
- Need model evaluation (PPC, WAIC, LOO)? → Model Assessment
- Need MCMC, HMC, or variational inference? → Computation
- Need variational inference in depth (ELBO, ADVI, VAEs, diagnostics) or neural simulation-based inference (NPE/NLE/NRE for simulators and ABMs)? → Variational Inference, Neural Simulation-Based Inference
- Need regression, GLMs, or missing data? → Regression Models
- Need GPs, mixtures, spatial, or causal BART? → Advanced Models
- Need Bayesian causal inference (potential outcomes, BART/BCF, IV, g-computation)? → Causal Inference
- Need the iterative modeling cycle, the full 2026 Bayesian Workflow textbook (79 notes incl. 16 case studies), or simulation-based calibration (SBC)? → Bayesian Workflow, starting at Bayesian Workflow Book - Overview
- Need likelihood-free / simulation-based inference for chaotic dynamic models (synthetic likelihood)? → Synthetic Likelihood
Book Overviews
- BDA3 - Overview — Master index for the textbook’s structure and key themes
- Statistical Rethinking - Overview — McElreath’s pedagogical Bayesian course with R and Stan
- Bayesian Workflow Book - Overview — Gelman, Vehtari & McElreath (2026): the workflow textbook, 31 chapters + 2 appendices, 79 notes
Sub-topics
| Sub-topic | Notes | Domain |
|---|---|---|
| Inference Fundamentals | 8 | Bayes’ theorem, conjugate models, hierarchical models (BDA3 Part I) |
| Model Assessment | 5 | Posterior predictive checks, model comparison, decision analysis (BDA3 Part II) |
| Computation | 21 | MCMC, HMC, variational inference, Stan (BDA3 Part III); Variational Inference sub-topic (8 notes: ELBO, CAVI, BBVI, ADVI, VAEs, flows, PSIS/VSBC diagnostics) and Neural Simulation-Based Inference sub-topic (8 notes: NPE/NLE/NRE, flows, amortized vs sequential, benchmarking, ABM calibration) |
| Regression Models | 9 | Bayesian regression, multilevel models, GLMs, missing data (BDA3 Part IV) |
| Advanced Models | 10 | GPs, mixtures, Dirichlet processes, spatial, copulas, BART, Bayesian IPW (BDA3 Part V + PyMC) |
| Bayesian Workflow | 92 | The 2026 Bayesian Workflow textbook in full (79 notes: foundations, model building and priors, evaluation and comparison, computation and failure modes, SBC, 16 case studies, 2 appendices) + the 2020 paper it expands (7 notes) + simulation-based calibration theory (Talts et al. 2018, 6 notes) |
| Causal Inference | 39 | Potential outcomes, BART/BCF outcome models, propensity score, IV, g-formula, metalearners, BSTS/CausalImpact, knowledge elicitation, and dynamic treatment regimes (Q-/A-learning) |
| Synthetic Likelihood | 4 | Likelihood-free inference for noisy chaotic dynamic models: phase-insensitive summary statistics, the MVN synthetic likelihood, MCMC exploration, Nicholson’s blowfly application (Wood 2010, Nature) |
Sources
- Wood 2010 - Statistical Inference for Noisy Nonlinear Ecological Dynamic Systems — Wood, S.N. (2010), Statistical inference for noisy nonlinear ecological dynamic systems, Nature 466(7310):1102–1104 (synthetic likelihood)
- BDA3 — Bayesian Data Analysis, 3rd Edition (Gelman, Carlin, Stern, Dunson, Vehtari, Rubin)
- Gelman Vehtari McElreath 2026 - Bayesian Workflow (book) — Gelman, Vehtari & McElreath (2026), Bayesian Workflow, 550 pp. (textbook)
- BayesWorkflow — Bayesian Workflow (Gelman, Vehtari, Simpson et al., 2020)
- Talts et al. - Simulation-Based Calibration — Talts, Betancourt, Simpson, Vehtari & Gelman (2018), “Validating Bayesian Inference Algorithms with Simulation-Based Calibration” (arXiv:1804.06788)
- StatRethink-Bayes — Statistical Rethinking (McElreath, 2015)
- How to use Bayesian propensity scores and inverse probability weights — Andrew Heiss (2021-12-18): Liao-Zigler Bayesian IPW in R/brms
- Li et al. - 2022 - Bayesian causal inference a critical review — Li, Ding & Mealli (2022): Bayesian causal inference critical review, Phil. Trans. R. Soc. A 381
See Also
- Research Methodology — Multiple comparisons, causal inference in advertising
- Econometrics — Frequentist/econometric perspective on causal inference
- Mostly Harmless Econometrics - Overview — Frequentist/econometric perspective on related topics