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Reconciling Bayesian and frequentist evidence in one-sided testing problem. (English) Zbl 0612.62021

Bayesian and frequentist testing of the hypothesis \(H_ 0: \theta \leq 0\) against \(H_ 1: \theta >0\), where \(\theta\) is an unknown parameter, are considered. The p-value from the frequentist inference is compared with the posterior probability that \(H_ 0\) is true given the data where the prior is from classes of priors which are defined as impartial i.e. that which give equal weight to both the null and alternative hypotheses. For many of these classes it is shown that the infimum of this posterior probability is equal to p and other cases less than p. It is shown by J. O. Berger and T. Sellke [see the following review, Zbl 0612.62022] that these inferences are irreconcilable if \(H_ 0\) is a point hypothesis.
Discussion of both papers appears after the paper of Berger and Sellke.
Reviewer: P.W.Jones

MSC:

62F03 Parametric hypothesis testing
62F15 Bayesian inference
62A01 Foundations and philosophical topics in statistics

Citations:

Zbl 0612.62022
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