Generative Model Design

Generative Model Design

Reference for specifying generative models and organizing experiments around a structural question. Read references on demand — each section below is a required decision when specifying a model; the principles and resolution-sequence references apply across the whole proposal.

For the upstream analysis-level decisions (analysis purpose, validation strategy, domain context, and the structural questions themselves), see analysis-design.

Key Practices

• Mixture model discipline. Every component must correspond to a named physical process. Never propose "K Normal components with unknown K" — it produces permutation symmetry and component collapse. Always require ordered[K] constraints on component location parameters. Use Hurdle vs Zero-Inflated, Censored vs Truncated based on the real generative story, not what's convenient.
• Prior geometry hazards. Never use inv_gamma for variance/scale hyperpriors (creates funnel + artificial lower bound) — prefer exponential, normal<lower=0>, or student_t(3, 0, s)<lower=0>. For correlation matrices use lkj_corr_cholesky(eta) with eta >= 2.
• Process model vs observation model. Separate the noiseless latent truth from the observation process (censoring, truncation, rounding, selection). Most likelihood mistakes conflate the two.

Spec references

Each section below is a required decision in a complete spec. Read on demand while specifying an experiment.

• references/setup.md — measurement story and observation-unit independence (§1-§2)
• references/likelihood.md — likelihood family, noise geometry, dispersion, zero/boundary processes (§3)
• references/pooling-hierarchy.md — pooling structure, grouping factors, what's hierarchical and why (§4)
• references/priors.md — prior implications on the observable scale, containment calibration, prior pushforward check (§5)
• references/identifiability.md — non-identifiability and computational risks; flag for downstream agents (§6)
• references/falsification.md — what would break this model — targeted PPC, ELPD resolution, parameter resolution (§7)

Design-discipline references

Cross-cutting principles and structure for experiment sets:

• references/design-principles.md — mechanistic parameterization, Recipe du Variate, broad family consideration, mixture discipline (deep dive). Apply to every spec.
• references/resolution-sequence.md — how to organize a set of experiments (shared baseline → core → variants; hierarchical progression; inferential-purpose constraints) so that comparisons answer a structural question.