Frequentist properties of bayesian multiplicity control for multiple testing of normal means

We consider the standard problem of multiple testing of normal means, ob-taining Bayesian multiplicity control by assuming that the prior inclusion probability (the assumed equal prior probability that each mean is nonzero) is unknown and assigned a prior distribution. The asymptotic frequentist behavior of the Bayesian procedure is studied, as the number of tests grows. Studied quantities include the false positive probability, which is shown to go to zero asymptotically. The asymptotics of a Bayesian decision-theoretic approach are also presented.

Duke Scholars

Author James O. Berger Statistical Science