Explanation: Prior Predictive Checking

Prior predictive checking tests whether configured priors imply plausible outcome behaviour before posterior interpretation.

In AMMM this check is a first-class artefact in 10_pre_diagnostics/.

Why It Matters

Parameter-scale priors can look reasonable while their joint implications for $y_t$ are unrealistic. Prior predictive checks catch this early.

This prevents spending compute on models that are implausible by construction.

AMMM Plausibility Ratio

AMMM samples from the prior predictive and computes a practical plausibility ratio:

$$ r_{\mathrm{plaus}} = \frac{1}{N} \sum_{i=1}^{N} \mathbf{1}\left[y_i^{\mathrm{prior}} \in \left[ y_{\min} - 2,s_y,; y_{\max} + 2,s_y \right]\right] $$

Where $y_{\min}$, $y_{\max}$, and $s_y$ come from observed training targets.

Operational guidance:

• r_plaus >= 0.5: broadly plausible prior predictive behaviour.
• r_plaus < 0.5: warning condition; priors should be reviewed.

Default sampling uses 500 prior predictive draws.

Stage Iteration Loop

Prior predictive checking creates an explicit iterate-before-fit loop:

1. Specify model and priors.
2. Run prior predictive check.
3. If implausible, revise priors and repeat.
4. Proceed to posterior interpretation only after plausibility is acceptable.

Artefacts

Artefact	Purpose
10_pre_diagnostics/prior_predictive_check.png	Visual comparison of prior predictive draws against observed range/mean.
10_pre_diagnostics/prior_predictive_summary.csv	Summary statistics for prior predictive versus observed target.

Scale Handling

When AMMM uses in-graph target standardisation, diagnostics are inverse-transformed so prior predictive checks are interpreted on the original business scale.

Gate Role

Prior predictive plausibility corresponds to gate g1 in the stage-gated workflow.

See Workflow Stages and Methodology.

Causal Caveat

Passing prior predictive checks indicates coherent prior implications, not causal identification.