Semiparametric Mixture Models and High-Dimensional Inference

• Activity Number: 642
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ryan Martin*+ and Surya T Tokdar
• Companies: University of Illinois at Chicago and Duke University
• Keywords: empirical Bayes ; high-dimensional ; mixture model ; multiple testing ; predictive recursion ; semiparametric

Abstract

The nonparametric empirical Bayes approach creates a link between mixture models and high-dimensional inference problems. In this talk I shall focus on a new empirical Bayes approach to large-scale multiple testing. The jumping off point is a new version of the two-groups model which is identifiable and guarantees the non-null density has heavier tails than the null. The underlying mixing distribution has both discrete and continuous parts, so a version of the predictive recursion (PR) marginal likelihood method is used to fit the model and define a decision rule. Illustrations on real and artificial data will be given. Time permitting, I will discuss other high-dimensional applications of PR marginal likelihood, including function estimation and variable selection in regression.