The Optimal Discovery Procedure and Bayesian Decision Rules

Peter Mueller
Department of Biostatistics
University of Texas
M.D. Anderson Cancer Center

Abstract

        We discuss an interpretation of the optimal discovery procedure (ODP, Storey 2006) as an approximate Bayes rule in a nonparametric Bayesian model for multiple comparisons.  An improved approximation defines a non-parametric Bayesian version of the ODP statistic (BODP).  The definition includes multiple shrinkage in clusters. In a simulation study and a data analysis example we show a (small) improvement in frequentist summaries. The BODP allows easy modifications for dependence of the comparisons and other extensions of the ODP.