  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
Pareto, and many other distributions. We prove some general asymptotic
optimality results under fixed and random thresholding. As examples of these
general results, we establish the Bayesian asymptotic optimality of several
multiple testing procedures in the literature 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.
