Applied Bayesian Nonparametrics

• Activity Number: 108
• Type: Invited
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Michael I. Jordan*+
• Companies: University of California at Berkeley

Abstract

Bayesian inference is often viewed as an assumption-laden approach to statistical inference, in which strong assumptions are imposed in order to support inference. The past two decades have seen the development of an increasingly vigorous field of Bayesian nonparametrics, which simultaneously provides an expressive language for prior specification and allows for weaker assumptions. Mathematically, Bayesian nonparametrics amounts to using general stochastic processes as prior distributions. I discuss a class of stochastic processes known as "completely random measures" that I view as providing a useful point of departure for a range of applications of Bayesian nonparametrics to problems in science and engineering. In particular I will present models based on the beta process, the Bernoulli process, the gamma process and the Dirichlet process, and on hierarchical and nesting constructions that use these basic stochastic processes as building blocks. I will discuss applications to a variety of scientific domains, including protein structural modeling, vision, speech and statistical genetics.