Single-Factor Transformation Priors for Density Regression

• Activity Number: 567
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Suprateek Kundu*+ and David Dunson
• Companies: The University of North Carolina at Chapel Hill and Duke University
• Keywords: Nonparametric Bayes ; Kernel estimation ; Density regression ; Gaussian process ; Latent variable model ; Dirichlet process

Abstract

Although mixture modeling has formed the backbone of the literature on Bayesian density estimation incorporating covariates, the use of mixtures leads to some well known disadvantages. Avoiding mixtures, we propose a flexible class of priors based on a random transformation of a uniform latent variable. These priors are related to Gaussian process latent variable models proposed in the machine learning literature. For density regression, we model the response and predictor means as distinct unknown transformation functions dependent on the same underlying latent variable, thus inducing dependence through a single factor. The induced prior is shown to have desirable properties including large support and posterior consistency. We demonstrate advantages over Dirichlet process mixture models in a variety of simulations, and apply the approach to an epidemiology application.