Abstract
We discuss a case study that highlights the features and limitations of a principled Bayesian decision theoretic approach to massive multiple comparisons. We consider inference for a mouse phage display experiment with three stages. The data are tripeptide counts by tissue and stage. The primary aim of the experiment is to identify ligands that bind with high affinity to a given tissue. The inference goal is to select from a large list of peptide and tissue pairs those with significant increase over stages. The desired inference summary involves a massive multiplicity problem. We consider two alternative approaches to address this multiplicity issue. First we propose an approach based on the control of the posterior expected false discovery rate. We notice that the implied solution ignores the relative size of the increase. This motivates a second approach based on a utility function that includes explicit weights for the size of the increase.