A Personal Survey of the Dirichlet Process and Its Role in Nonparametrics

• Activity Number: 512
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Noether Award Committee
• Author(s): Jayaram Sethuraman*+
• Companies: Florida State University

Abstract

Following standard parametric Bayes applications, there was a growing need for nonparametric Bayes analysis which seemed to pose some difficulties. These difficulties were removed by the first definitions of Dirichlet processes by Ferguson, Blackwell and MacQueen.

Dirichlet processes became famous after some easy applications in standard nonparametric Bayes problems. However, though the proofs looked complicated and mystifying, many salient properties of Dirichlet processes were being established.

The Sethuraman constructive definition of a Dirichlet process simplified proving such properties and establishing some further ones.

Computational Bayes analysis took off in parametric problems, thanks to MCMC. The importance of this constructive definition for computational nonparametric Bayes analysis was recognized immediately and it opened the flood gates for a multitude of diverse applications.

Some of these developments along with some new applications of the constructive definition are presented here.