Consistency of the Frequentist and Bayesian Evidence in the One-Sided Testing Problems Under Normal Models

The agreement or reconcilability of the frequentist and Bayesian evidence in testing statistical hypotheses is commonly concerned by both the frequentist and the Bayesian school. For the one-sided hypothesis testing problem in the presence of nuisance parameters under normal distributions, the p-value and the Bayesian evidence against the null hypothesis were studied. It is shown that, for a variety of testing problems, these two kinds of evidence can reach an agreement.