In this talk, a novel framework for multiple testing of hypotheses grouped in a one-way classified form using hypothesis-specific local false discovery rates (Lfdr’s) is given. It is built on an extension of the standard two-class mixture model from single to multiple groups, defining hypothesis-specific Lfdr as a function of the conditional Lfdr for the hypothesis given that it is within a significant group and the Lfdr for the group itself and involving a new parameter that measures grouping effect. This definition captures the underlying group structure for the hypotheses belonging to a group more effectively than the standard two-class mixture model. Two new Lfdr based methods, possessing meaningful optimalities, are produced in their oracle forms. One, designed to control false discoveries across the entire collection of hypotheses, is proposed as a powerful alternative to simply pooling all the hypotheses into a single group and using commonly used Lfdr based method under the standard single-group two-class mixture model. The other is proposed as an Lfdr analog of the method of Benjamini & Bogomolov (2014) for selective inference. It controls Lfdr based measure of false discoveries associated with selecting groups concurrently with controlling the average of within-group false discovery proportions across the selected groups. Numerical studies show that our proposed methods are indeed more powerful than their relevant competitors, at least in their oracle forms, in commonly occurring practical scenarios.

Dr. Sanat K. Sarkar is an internationally recognized researcher who has made fundamental contributions to the development of the field of multiple testing toward its applications in modern scientific investigations, such as in genomics and brain imaging. His research has been funded by the National Science Foundation and the National Security Agency, and often been cited in peer-reviewed journals. He has delivered invited talks at numerous national and international conferences. He co-organized a major conference on Multiple Comparisons funded by the NSF-CBMS and served on the organizing committees of several international conferences on the same topic. He has served on the editorial boards of several respectable journals, like the Annals of Statistics, the American Statistician, and Sankhya. Dr. Sarkar has been recognized as a fellow by both the Institute of Mathematical Statistics and the American Statistical Association, and as an elected member of the International Statistical Institute. He was awarded the Musser Award for excellence in research by the Fox School and inducted several times to the Dean’s Research Honor Roll.