Index: Case Studies

Case Studies

Routing Summary

Part 4 (Chapters 16–31) of Gelman, Vehtari & McElreath (2026). Sixteen complete analyses, each recording the model specification, what went wrong, and the transferable lesson. Route by the problem you are having, not by the application domain.

• Chains won’t mix / aliasing → Sampling Problems with Latent Variables - No Vehicles in the Park, Debugging a Model - World Cup Football
• Multimodal posterior → Challenge of Multimodality - Differential Equation for Planetary Motion
• Which prior for many coefficients → Models for Regression Coefficients - Student Grades, Prior Specification for Regression Models - Sleep Study
• Reading Pareto $\hat{k}$ and p_loo → LOO Model Checking and Comparison - Roaches
• Building a model in steps → Coding a Series of Models - Movie Ratings, Incremental Development and Testing - Black Cat Adoptions, Building Up to a Hierarchical Model - Coronavirus Testing
• Physical/mechanistic modeling beats curve fitting → Model Building and Expansion - Golf Putting
• Latent variables with real interpretation → Model Building with Latent Variables - Animal Movement
• Additive decomposition and GP approximation → Model Building - Time-Series Decomposition for Birthdays
• Verifying a Stan program is correct → Simulation-Based Calibration Checking in Model Development Workflow
• Graphical posterior predictive checks → Posterior Predictive Checking - Stochastic Learning in Dogs
• Comparing models predictively → Predictive Model Checking and Comparison - Clinical Trial
• Using a fit to make a decision → Using a Fitted Model for Decision Analysis - Classification Competition

Concept Map

Ch.	Case study	Domain	What went wrong	Lesson
16	Coding a Series of Models - Movie Ratings	Ratings	—	A model is a sequence, not an artifact
17	Prior Specification for Regression Models - Sleep Study	Psychology	Default priors too weak	Priors are part of the model
18	Predictive Model Checking and Comparison - Clinical Trial	Medicine	—	Checks drive comparison
19	Building Up to a Hierarchical Model - Coronavirus Testing	Epidemiology	Pooling choices misstate uncertainty	Earn the hierarchy incrementally
20	Using a Fitted Model for Decision Analysis - Classification Competition	Competition	—	Inference is not the endpoint
21	Posterior Predictive Checking - Stochastic Learning in Dogs	Animal learning	Model misses the learning curve	What a graphical check reveals
22	Incremental Development and Testing - Black Cat Adoptions	Animal shelter	Bugs hidden by aggregate fit	Test each component as added
23	Debugging a Model - World Cup Football	Sport	A real bug in a believed model	Debug the model, not just the code
24	LOO Model Checking and Comparison - Roaches	Pest control	High Pareto $\hat{k}$, large p_loo	Read CV diagnostics before elpd
25	Model Building and Expansion - Golf Putting	Sport	Flexible curve fits worse than geometry	Mechanistic structure beats flexibility
26	Model Building with Latent Variables - Animal Movement	Ecology	Latent states weakly identified	Latents need interpretable structure
27	Model Building - Time-Series Decomposition for Birthdays	Demography	Double intercept; overshrunk 13th; “ringing”	Centered can beat non-centered; state your failures
28	Models for Regression Coefficients - Student Grades	Education	Flat prior: $R^2$ 0.32 vs. LOO-$R^2$ 0.19	Good priors remove the need for selection
29	Sampling Problems with Latent Variables - No Vehicles in the Park	Survey	Three-way additive aliasing	Sum-to-zero constraint; centered beat non-centered
30	Challenge of Multimodality - Differential Equation for Planetary Motion	Physics	Approximate aliasing from a cyclical orbit	Pathfinder initialization; minor modes trap chains
31	Simulation-Based Calibration Checking in Model Development Workflow	Synthetic	Five separate bugs	SBC as a development subroutine

Notes

• Coding a Series of Models - Movie Ratings — CONTAINS: Figures 16.1–16.5; Ch. 16
• Prior Specification for Regression Models - Sleep Study — CONTAINS: Figures 17.1–17.12; Ch. 17
• Predictive Model Checking and Comparison - Clinical Trial — CONTAINS: Figures 18.1–18.12; Ch. 18
• Building Up to a Hierarchical Model - Coronavirus Testing — CONTAINS: Eq. 19.1–19.3; Figures 19.1–19.5; Ch. 19
• Using a Fitted Model for Decision Analysis - Classification Competition — CONTAINS: Figures 20.1–20.2; Ch. 20
• Posterior Predictive Checking - Stochastic Learning in Dogs — CONTAINS: Figures 21.1–21.14; Ch. 21
• Incremental Development and Testing - Black Cat Adoptions — CONTAINS: Eq. 22.1–22.3; Figures 22.1–22.3; Ch. 22
• Debugging a Model - World Cup Football — CONTAINS: Figures 23.1–23.6; Ch. 23
• LOO Model Checking and Comparison - Roaches — CONTAINS: Figures 24.1–24.21; Pareto $\hat{k}$, p_loo, moment matching, integrated LOO; Ch. 24
• Model Building and Expansion - Golf Putting — CONTAINS: Figures 25.1–25.10; the geometric model; Ch. 25
• Model Building with Latent Variables - Animal Movement — CONTAINS: Eq. 26.1–26.3; Figures 26.1–26.10; Ch. 26
• Model Building - Time-Series Decomposition for Birthdays — CONTAINS: Eq. 27.1–27.3; Figures 27.1–27.16; Hilbert-space GP, four-rung approximate ladder, regularized horseshoe; Ch. 27
• Models for Regression Coefficients - Student Grades — CONTAINS: Figures 28.1–28.14; piranha principle, R2D2, projpred; Ch. 28
• Sampling Problems with Latent Variables - No Vehicles in the Park — CONTAINS: Figures 29.1–29.5; sum_to_zero_vector, centered vs. non-centered, full Stan programs; Ch. 29
• Challenge of Multimodality - Differential Equation for Planetary Motion — CONTAINS: Figures 30.1–30.5; Hamilton’s equations, approximate aliasing, Pathfinder; Ch. 30
• Simulation-Based Calibration Checking in Model Development Workflow — CONTAINS: Figures 31.1–31.11; five bugs, the Fano-factor filter, coverage plots; Ch. 31

Sources

• Gelman Vehtari McElreath 2026 - Bayesian Workflow (book) — Chapters 16–31, pp. 263–482

See Also

• Bayesian Workflow Book - Overview — the book’s routing index
• Computational Workflow — the theory the computational case studies exercise
• Evaluating and Comparing — the theory the checking case studies exercise
• Building Models — the theory the prior-specification case studies exercise