On the d-posterior approach to the multiple testing problem

Abstract

The problem of multiple testing is considered as a special case of the problem of guaranteed discrimination of hypotheses in a d-posterior approach. This approach is based on the Bayesian paradigm and applies only to the situation where there is a real sequence of statistical experiments that lead to a decision. A restriction on the d-posterior risk of the first kind, i.e. on the rate of correct null hypotheses, with the proviso that the statistical experiment led to its rejection, is guaranteed. The possibilities of this approach are illustrated through the example of the problem of distinguishing genes with increased expression. We propose a general Bayesian model for solving similar problems. In particular, the problem of hyperactive and repressed gene selection is solved. Unlike traditional methods of multiple testing, there is also the possibility to distinguish more than two hypotheses, such as, genes with unchanged, increased, or decreased expression.