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](references/elicitation.md) — a complete prior-predictive example, unit conversions, expert workflow, analytic checks and power reweighting. - [Shrinkage and regularization](references/shrinkage.md) — regularized horseshoe scales, R2D2 variance allocation, geometry and interpretation. Use the installed package's version-matched API documentation when adapting the examples. PreliZ widgets need an interactive notebook; pymc-extras is optional and only needed for its R2D2 helper. This skill does not require another skill.