An optimal procedure for multiple hypotheses testing

The most traditional approach to the problem of multiple hypotheses testing has been Bonferroni’s method but, in the last years, a lot of attention has been paid to Benjamini–Hochberg’s method. In this article, a general procedure is considered, where the prior information (when available) and the cost of erroneous decisions are incorporated in a setting of Bayesian decision theory. The main result in the paper is a theorem, where the existence of an optimal procedure is proved, and an explicit formulation for this optimal procedure is given.