Bayesian Decision Theory for Multiple Comparisons

Charles Lewis
Fordham University
Educational Testing Service

Abstract

            A loss function related to the directional false discovery rate (DFDR) criterion for evaluating multiple comparisons procedures is introduced.  The Bayes decision rule for this loss is obtained.  When used with a vague prior, this Bayes rule is shown to be very similar to the sampling theory procedure introduced by Benjamini and Hochberg to control the FDR.  This provides a new perspective on the properties of FDR-controlling procedures.