Wednesday, September 2, 2009
03:30 PM in REC 315
Professor Jayanta Ghosh
Department of Statistics, Purdue University

Multiple Tests for Microarrays, Mixture Models, Bayes Oracle and (Asymptotic) Optimality of the Benjamini Hochberg Test

Abstract

I will introduce the problem of high dimensional multiple testing, which has become popular in microarrays and many other areas, see for example Efron (Statistical Science, 2008). Efron's model is nonparametric. I will use instead another popular parametric model and discuss use of FDR (False Discovery Rates), the Benjamini Hochberg rule for multiple test and a host of other tests. Many concrete applications, unpublished talk by Benjamini at the last Purdue Symposium (2003), and some theory based on estimation, coming from Stanford, show the importance of the BH multiple test. On the other hand, Bayesian decision theorists have pointed out that test is not easy to justify from a decision theoretic approach to testing.

I will discuss these issues briefly and then, drawing on new joint work with Professors Malgorzata Bogdan, Arijit Chakrabarti and Florian Frommlet, will present a popular mixture model approach to multiple testing. This will lead to what we call a Bayesian Oracle and results that show the BH test is asymptotically as good as the Bayes Oracle (under appropriate conditions). This would be done in two lectures on September 2 and September 9. On September 14, Professor Bogdan will continue the discussion.

My presentations will stress heuristics and intution rather than technical details.