Bayesian and Frequentist Handling of Multiple Testing

        It has been frequently asserted that Bayesian methods for multiple testing ignore the multiplicity issue; also that FDR can be interpreted in a Bayesian fashion. In this talk we address these issues while reviewing recent and popular methods to address multiple testing . We consider both Bayesian and Frequentist methods, as well as eclectic ones that seem to combine both approaches; in particular, we demonstrate how Bayesian analysis handles multiplicities, and we look at  methods based on some type of False Discover Rate error. The main goal is to gain understanding of these methods from both a Bayesian perspective and a decision-theoretic perspective. For instance, a key question is whether FDR can arise naturally in a decision setting. This talk summarizes a variety of issues about multiple testing discussed during the SAMSI Summer Program on Multiplicity and Replicability in Scientific Studies.