Reconciling Bayesian and Frequentist Evidence in the One-Sided Testing Problem

George Casella, Roger L. Berger
1987 Journal of the American Statistical Association  
For the one-sided hypothesis testing problem it is shown that it is possible to reconcile Bayesian evidence against H0, expressed in terms of the posterior probability that Ho is true, with frequentist evidence against H0, expressed in terms of the p value. In fact, for many classes of prior distributions it is shown that the infimum of the Bayesian posterior probability of Ho is equal to the p value; in other cases the infimum is less than the p value. The results are in contrast to recent
more » ... trast to recent work of Berger and Sellke (1987) in the two-sided (point null) case, where it was found that the p value is much smaller than the Bayesian infimum. Some comments on the point null problem are also given.
doi:10.2307/2289130 fatcat:4j7r6wj77nb43ntry2jie7vr54