Bayesian Model-Based Approaches to Semiparametric and Nonparametric Quantile Regression

• Activity Number: 398
• Type: Invited
• Date/Time: Wednesday, August 1, 2007 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Athanasios Kottas*+ and Milovan Krnjajic and Matthew Taddy
• Companies: University of California, Santa Cruz and Lawrence Livermore National Laboratory and University of California, Santa Cruz
• Keywords: Censored quantile regression ; Dirichlet process mixture models ; Markov chain Monte Carlo ; Multivariate normal mixtures ; Scale uniform mixtures

Abstract

We present two approaches to Bayesian quantile regression, using Dirichlet process (DP) mixture models. We first consider a semiparametric additive formulation, with the regression function modeled parametrically and with nonparametric priors for the error distribution. The prior models include dependent DPs resulting in error distributions that can change nonparametrically with the covariates. The second line of research develops a flexible fully nonparametric approach to inference for any set of quantiles of the response distribution. Under this approach, the joint distribution of the response and the covariates is modeled with a DP mixture, with posterior inference for different quantile curves emerging through the conditional distribution of the response given the covariates. Inference (possibly, under censoring) is implemented using posterior simulation methods for DP mixtures.