Maximum Likelihood for Nonparametric Empirical Bayes: New Methods and Applications

• Activity Number: 119
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Lee H. Dicker*
• Companies: Rutgers University
• Keywords: Mixture models ; Nonparametric ; Convex optimization ; Empirical Bayes ; Maximum likelihood

Abstract

Empirical Bayes methods have a long and rich history in statistics, and are particularly well-suited for many high-dimensional problems, which are important in modern data analysis. Nonparametric maximum likelihood (NPML) is one elegant approach to empirical Bayes that has been studied since the 1950s (Robbins, 1950; Kiefer & Wolfowitz, 1956). However, implementation and analysis of NPML-based methods for empirical Bayes is notoriously difficult. Recent computational breakthroughs have greatly simplified the implementation of NPML-based methods. Leveraging these recent advances, we have developed a variety of promising and flexible new methods involving NPML for empirical Bayes. In this talk, we will discuss these methods, along with applications in a variety of problems, including classification, regression, and multivariate density estimation. This is joint work with Sihai Dave Zhao (UIUC) and Long Feng (Rutgers).