Bayesian Multiple Testing Under Sparsity for Polynomial-Tailed Distributions

• Activity Number: 258
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Xueying Tang* and Ke Li and Malay GHosh
• Companies: University of Florida and Southwestern University of Finance and Economics and University of Florida
• Keywords: asymptotic optimality ; multiple testing ; false discovery rate ; polynomial-tailed distributions

Abstract

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 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 proposed by Benjamini and Hochberg (1995), Efron and Tibshirani (2002), Genovese and Wasserman (2002) and others 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.