Index: Foundations

Foundations

Routing Summary

Part 1 (Chapters 1–4) of Gelman, Vehtari & McElreath (2026). Covers why Bayes, what “Bayesian” even means, why no method is assumption-free, the master workflow diagram, the four-scenario taxonomy that organizes the book, and two complete introductory examples. 8 notes.

• Need the master workflow diagram (Figure 2.1)? → From Inference to Data Analysis to Workflow
• Need the cost-benefit case for Bayes? → Why Bayes - Benefits, Costs, and Borders
• Need to know which of subjective/objective/pragmatic Bayes the book adopts? → Varieties of Bayesian Theory
• Need the argument that non-Bayesian methods carry assumptions too? → There Is No Safe Haven
• Need the taxonomy that organizes the whole book? → Four Modeling Scenarios
• Need Stan/PPL setup and the vocabulary of probabilistic programming? → Computational Tools and Probabilistic Programming
• Need a first, minimal Stan program? → Bioassay - A First Probabilistic Program
• Need one problem carried end to end through the entire workflow? → Multiple-Choice Exam - A Full Workflow Walkthrough

Concept Map

Concept	Note	Type	Depends On	Key Result
Benefits, costs, and borders of Bayesian inference	Why Bayes - Benefits, Costs, and Borders	concept	—	Bayes pays where prior information and uncertainty propagation matter; costs are computational and modeling effort
Subjective / objective / pragmatic Bayes	Varieties of Bayesian Theory	concept	Why Bayes - Benefits, Costs, and Borders	The book takes a pragmatic, falsificationist stance
No assumption-free method	There Is No Safe Haven	concept	Varieties of Bayesian Theory	Every method encodes assumptions; the choice is whether they are explicit
Figure 2.1 master workflow diagram	From Inference to Data Analysis to Workflow	concept	Why Bayes - Benefits, Costs, and Borders	Inference ⊂ data analysis ⊂ workflow; transcribed as mermaid
Four modeling scenarios	Four Modeling Scenarios	definition	From Inference to Data Analysis to Workflow	The taxonomy that determines which workflow steps apply
Probabilistic programming, Stan	Computational Tools and Probabilistic Programming	reference	—	The tooling assumed throughout the book
Bioassay logistic model	Bioassay - A First Probabilistic Program	example	Computational Tools and Probabilistic Programming	A complete first Stan program with prior, fit, and check
Full workflow walkthrough	Multiple-Choice Exam - A Full Workflow Walkthrough	example	all of the above	Every step of Figure 2.1 exercised on one dataset

Notes

• Why Bayes - Benefits, Costs, and Borders — CONTAINS: the benefits/costs ledger; where Bayesian methods stop paying off; Ch. 1.1
• Varieties of Bayesian Theory — CONTAINS: subjective, objective, and pragmatic Bayes; the book’s stated position; Ch. 1.2
• There Is No Safe Haven — CONTAINS: the argument that all inference is assumption-laden; Ch. 1.3–1.5
• From Inference to Data Analysis to Workflow — CONTAINS: Figure 2.1 transcribed as a mermaid diagram, Figure 2.2, the three nested scopes; Ch. 2.1–2.2
• Four Modeling Scenarios — CONTAINS: the four-scenario taxonomy and what each implies for workflow; Ch. 2.3–2.5
• Computational Tools and Probabilistic Programming — CONTAINS: Stan, rstanarm, brms, cmdstanr; the modeled/unmodeled distinction in code; Ch. 3.1–3.4
• Bioassay - A First Probabilistic Program — CONTAINS: full Stan program, prior specification, posterior summary; Figures 3.1, 3.2; Ch. 3.5–3.6
• Multiple-Choice Exam - A Full Workflow Walkthrough — CONTAINS: 16 figures’ worth of a single problem carried through prior predictive checking, fitting, diagnostics, posterior predictive checking, expansion, and comparison; Ch. 4

Sources

• Gelman Vehtari McElreath 2026 - Bayesian Workflow (book) — Chapters 1–4, pp. 3–60

See Also

• Building Models — where the workflow goes next
• Bayesian Workflow Book - Overview — the book’s routing index
• Statistical and Computational Workflow for Bayesians and Non-Bayesians — the non-Bayesian translation of these foundations