Bayesian density regression

Summary. This article considers Bayesian methods for density regression, allowing a random probability distribution to change flexibly with multiple predictors. The conditional response dis-tribution is expressed as a nonparametric mixture of regression models, with the mixture distribu-tion changing with predictors. A class of weighted mixture of Dirichlet process (WMDP) priors is proposed for the uncountable collection of mixture distributions. It is shown that this specification results in a generalized Pólya urn scheme, which incorporates weights dependent on the distance between subjects ’ predictor values. To allow local dependency in the mixture distributions, we propose a kernel-based weighting scheme. A Gibbs sampling algorithm is developed for posterior computation. The methods are illustrated using simulated data examples and an epidemiologic application