COHERENCE OF THE POSTERIOR PREDICTIVE P-VALUE BASED ON THE POSTERIOR ODDS.

Abstract

It is well-known that classical p-values sometimes behave incoherently for testing hypotheses in the sense that, when '0 0 T .T , the support given to 0 T is greater than or equal to the support given to '0 T . This problem is also found for posterior predictive p-values (a Bayesian-motivated alternative to classical p-values). In this paper, it is proved that, under some conditions, the posterior predictive p-value based on theposterior odds is coherent, showing that the choice of a suitable discrepancy variable is crucial.