The Agreement between the Generalized p Value and Bayesian Evidence in the One-Sided Testing Problem

Abstract

In the problem of testing one-sided hypotheses, a frequentist may measure evidence against the null hypothesis by the p value, while a Bayesian may measure it by the posterior probability that the null hypothesis is true. In this paper, we consider the relationship between the generalized p value and the Bayesian evidence in testing one-sided hypotheses in the presence of nuisance parameters. The sufficient conditions for the agreement between these two kinds of evidence are given. Some examples are provided to show the agreement of Bayesian and frequentist evidence in many classical testing problems. This is an illustration of reconcilability of evidence in a general framework where the nuisance parameters are present.