Local-Mass Preserving Prior Distributions for Nonparametric Bayesian Models

• Activity Number: 509
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ju Hee Lee*+ and Steven MacEachern
• Companies: The Ohio State University and The Ohio State University
• Keywords: Local-Mass ; Nonparametric ; Bayes ; Dirichlet Process

Abstract

We address the problem of prior specification for models involving the Dirichlet process. We introduce the concept of local mass (the mass assigned by a prior for any given small region of the parameter space) to this prior specification problem, and propose a class of priors that focus on local mass. To specify such a prior, we carefully consider behavior of parameters of interest in some small region, and select a prior which preserves mass in the region. Local mass preservation ties the mass of the base measure to its dispersion, resulting in robust inference. Our strategy of constructing a prior can be applied to any Dirichlet process model. Calibration of the prior distribution is considered. We compare its performance to that of similar models with traditional prior distributions. The impact of choice of a prior on inference is discussed.