Predictive discrepancy statistic
= Predictive discrepancy statistic
{title2=$T(X)$}
A measurable summary of a possible dataset is chosen to detect disagreement with a specified predictive model. Compare its observed value with its distribution under replicated datasets. Large-discrepancy statistics can be checked with $\mathbb P(T(X^{\mathrm{rep}})\ge T(x))$. A <posterior predictive check> integrates over posterior parameter uncertainty; a fully specified null instead supplies a fixed reference law.