Building Models
Routing Summary
Part 2 (Chapters 5–7) of Gelman, Vehtari & McElreath (2026): choosing and specifying a model, every prior-choice rule the book states, simulation as a modeling tool, and the extension from inference to generalization, causal inference, and decision. 19 notes.
- Need where to start? → Choosing an Initial Model
- Need to translate subject-matter assumptions into a model? → Relating a Model to Subject-Matter Assumptions
- Need the formal specification of a Bayesian model? → Expressing a Bayesian Model with Probability Distributions
- Need why the data model is more than a likelihood? → A Data Model Is Not Just a Likelihood
- Need prior choice rules? → Prior Distributions (general), Constructing Priors for Effect Sizes (scaling), Joint Priors and Covariance Matrices (LKJ, horseshoe, R2D2)
- Need to check a prior before seeing data? → Prior Predictive Checking
- Need what happens when prior and likelihood disagree? → Tail Behavior and Prior-Likelihood Conflict
- Need simulation as a modeling tool? → Simulation to Express Uncertainty, Designing Simulated-Data Experiments
- Need generalization to a new population? → Poststratification
- Need causal inference? → Causal Inference as Generalization
- Need decision analysis? → From Inference to Decision
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| Where to start a model | Choosing an Initial Model | concept | Four Modeling Scenarios | Start simple enough to fit, complex enough to be relevant |
| Assumptions → model | Relating a Model to Subject-Matter Assumptions | concept | Choosing an Initial Model | Model structure should encode substantive claims |
| Formal specification | Expressing a Bayesian Model with Probability Distributions | definition | — | Joint and its decomposition |
| Data model ≠ likelihood | A Data Model Is Not Just a Likelihood | concept | Expressing a Bayesian Model with Probability Distributions | The same plays two roles |
| Generative vs. partially generative | Generative and Partially Generative Models | definition | A Data Model Is Not Just a Likelihood | Only fully generative models support prior predictive simulation |
| Prior choice | Prior Distributions | concept | Expressing a Bayesian Model with Probability Distributions | Weakly informative as default; the flat prior is not neutral |
| Effect-size scaling | Constructing Priors for Effect Sizes | concept | Prior Distributions | Standardize, then place the prior on an interpretable scale |
| Joint priors | Joint Priors and Covariance Matrices | definition | Prior Distributions | LKJ for correlation matrices; horseshoe and R2D2 for coefficient vectors |
| Data model + prior together | Specifying the Data Model and the Prior | concept | Prior Distributions | The pair, not either alone, defines the model |
| Modeled vs. unmodeled data | Modeled and Unmodeled Data | definition | Expressing a Bayesian Model with Probability Distributions | What you condition on vs. what you model |
| Prior predictive checking | Prior Predictive Checking | concept | Generative and Partially Generative Models | Simulate from the prior; look at the implied data |
| Prior-likelihood conflict | Tail Behavior and Prior-Likelihood Conflict | theorem | Prior Predictive Checking | Tail behavior determines which source wins under conflict |
| Simulation for uncertainty | Simulation to Express Uncertainty | concept | — | Propagate draws rather than combining standard errors |
| Point estimates | Point Estimates and Uncertainties | concept | Simulation to Express Uncertainty | When a summary is enough and when it misleads |
| Simulated-data experiments | Designing Simulated-Data Experiments | concept | Simulation to Express Uncertainty | Design the experiment, not just the simulation |
| Full-pipeline simulation | Simulating an Underlying Process, Data Collection, and Inference | example | Designing Simulated-Data Experiments | Simulate process, collection, and inference together |
| Poststratification | Poststratification | definition | Simulation to Express Uncertainty | MRP: model at the cell level, reweight to the population |
| Causal inference | Causal Inference as Generalization | concept | Poststratification | SATE/PATE as prediction under counterfactual predictors |
| Decision | From Inference to Decision | concept | Causal Inference as Generalization | Expected utility averaged over the posterior |
Notes
- Choosing an Initial Model — CONTAINS: the starting-point criteria; Figure 5.1; Ch. 5 intro, 5.1
- Relating a Model to Subject-Matter Assumptions — CONTAINS: Figure 5.2; Ch. 5.2
- Expressing a Bayesian Model with Probability Distributions — CONTAINS: the joint-distribution formalism; Ch. 5.3
- A Data Model Is Not Just a Likelihood — CONTAINS: the two readings of ; Ch. 5.4
- Generative and Partially Generative Models — CONTAINS: the definition and what each supports; Ch. 5.5
- Prior Distributions — CONTAINS: weakly informative priors, the flat-prior critique, prior scaling rules; Ch. 5.6
- Constructing Priors for Effect Sizes — CONTAINS: Figures 5.3, 5.4; standardization conventions; Ch. 5.6
- Joint Priors and Covariance Matrices — CONTAINS: Eq. 5.3; LKJ, regularized horseshoe, R2D2; Ch. 5.6
- Specifying the Data Model and the Prior — CONTAINS: the joint specification workflow; Ch. 5.7
- Modeled and Unmodeled Data — CONTAINS: the distinction in Stan terms; Ch. 5.8
- Prior Predictive Checking — CONTAINS: Figures 5.5–5.8; the full procedure; Ch. 5.9
- Tail Behavior and Prior-Likelihood Conflict — CONTAINS: Figures 5.9–5.13; which tail dominates; Ch. 5.10
- Simulation to Express Uncertainty — CONTAINS: Figure 6.1; Ch. 6.1
- Point Estimates and Uncertainties — CONTAINS: Figure 6.2; Ch. 6.2
- Designing Simulated-Data Experiments — CONTAINS: Figure 6.3; design principles for fake-data experiments; Ch. 6.3
- Simulating an Underlying Process, Data Collection, and Inference — CONTAINS: Figures 6.4–6.6; Ch. 6.4–6.5
- Poststratification — CONTAINS: Eq. 7.1–7.2; Figures 7.1–7.6; MRP; Ch. 7 intro, 7.1
- Causal Inference as Generalization — CONTAINS: Figures 7.7, 7.8; SATE and PATE; Ch. 7.2
- From Inference to Decision — CONTAINS: Figure 7.9; expected utility; Ch. 7.3–7.4
Sources
- Gelman Vehtari McElreath 2026 - Bayesian Workflow (book) — Chapters 5–7, pp. 63–134
See Also
- Foundations — the framing these chapters build on
- Evaluating and Comparing — what to do once the model is fit
- Prior Specification for Regression Models - Sleep Study — the case study for Chapter 5’s prior material
- Models for Regression Coefficients - Student Grades — R2D2 and horseshoe priors in practice
- Using a Fitted Model for Decision Analysis - Classification Competition — the case study for Chapter 7’s decision material