Prior Elicitation

Prior elicitation

A prior is a scientific assumption, not a scale-free default. Work from the quantity's meaning to a distribution, then check its observable implications.

Workflow

1. Define the quantity. Establish the estimand, population, support, units, transformation/link, reference predictor values and information available before outcomes. Separate physical bounds from high-probability intervals, parameter uncertainty from future-observation variability, and independent prior information from outcome-based scaling.
2. Elicit, do not invent. Ask for quantiles, probabilities, meaningful predictor contrasts and tail judgments; record their source and disagreements. Label teaching numbers as illustrative assumptions. Do not tune priors to held-out outcomes or fabricate expert answers.
3. Translate and check. Use analytic formulas or PreliZ maxent/quartile. Inspect optimizer status and achieved CDFs independently. Maximum entropy is conditional on a chosen family and parameterization, not universally noninformative. Prefer PreliZ over deprecated pm.find_constrained_prior.
4. Simulate prior predictions. Use pm.sample_prior_predictive(draws=...); access the resulting DataTree with prior["prior_predictive"]. Check support, conditional scales, dataset extremes and scientific contrasts against stated plausibility judgments, beyond observed-range coverage. Revisit assumptions when predictions are implausible, preserving support and simulation uncertainty. These are plausibility checks, not SBC of an inference implementation.
5. Assess reasonable alternatives. Vary plausible scales and tails while holding data, likelihood, transformations and estimand fixed for a prior sensitivity comparison. Rough exploratory fits can flag which assumptions to investigate; diagnose every posterior supporting reported conclusions with divergences, rank R-hat, bulk/tail ESS, estimand-specific MCSE and trace/rank plots.
6. Report the actual sensitivity. Compare physical-scale effects, meaningful event probabilities, uncertainty intervals and new-observation predictions. Stable answers over a few priors do not prove data dominance, global robustness or model adequacy. Power sensitivity is local and also needs reliable importance weights; its heuristic labels are not scientific decisions.

References

• Elicitation, PreliZ, prior predictions and sensitivity — a complete prior-predictive example, unit conversions, expert workflow, analytic checks and power reweighting.
• Shrinkage and regularization — regularized horseshoe scales, R2D2 variance allocation, geometry and interpretation.
• For optional pymc-extras prior factories, serialization, censoring and posterior-as-prior transfer, see extras model tools when pymc-modeling is installed.

Use the installed package's version-matched API documentation when adapting the examples. PreliZ widgets need an interactive notebook; pymc-extras is optional and needed only for its R2D2 helper or optional factory workflows. The elicitation and shrinkage references remain usable without another skill.