A Nonparametric Empirical Bayes Framework for Simultaneous Significance Testing

• Activity Number: 200
• Type: Topic Contributed
• Date/Time: Monday, August 3, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ryan Martin*+ and Surya T. Tokdar and Surya T. Tokdar
• Companies: Purdue University and Carnegie Mellon University and Carnegie Mellon University
• Keywords: empirical Bayes ; false discovery rate ; gene expression ; mixture models ; multiple testing ; two-groups model

Abstract

In this era of high-dimensional problems, simultaneous significance testing has become an important area of statistical research. Empirical Bayes methods, which thrive on the high-dimensionality by allowing for information sharing between cases, have received a lot of attention recently. Building on ideas of Efron and from Dirichlet process mixtures (DPMs), we construct a version of the popular two-groups model which is both flexible and identifiable. For inference, we propose an extension to M.A. Newton's predictive recursion (PR) which can efficiently estimate each model parameter, even the nonparametric mixing distribution. Motivation for this new algorithm comes from a connection between PR and DPMs and also from a new robustness theorem for the PR estimates. The resulting empirical Bayes testing procedure is applied to two popular gene expression data sets.