Bayesian Multiple Testing Under Sparsity for Polynomial-Tailed Distributions

This paper considers Bayesian multiple testing under sparsity for polynomial-tailed distributions satisfying a monotone likelihood ratio property. Included in this class of distributions are the Student's T, the half-T, the Pareto, the generalized double Pareto, and many other important distributions. We have proved some general asymptotic optimality results under fixed and random thresholding. As examples of these general results, we have established Bayesian asymptotic optimality of several multiple testing procedures for appropriately chosen false discovery rate levels. We also show by simulation that the Benjamini-Hochberg procedure with a false discovery rate level different from the asymptotically optimal one can lead to high Bayes risk.