Multiple testing using the posterior probabilities of directional alternatives, with application to genomic studies

This paper aims to connect Bayesian analysis and frequentist theory in the context of multiple comparisons. The authors show that when testing the equality of two sample means, the posterior probability of the one‐sided alternative hypothesis, defined as a half‐space, shares with the frequentist P ‐value the property of uniformity under the null hypothesis. Ultimately, the posterior probability may thus be used in the same spirit as a P ‐value in the Benjamini‐Hochberg procedure, or in any of its extensions.