Bayesian density regression

David B. Dunson, Natesh Pillai and Ju‐Hyun Park

Journal of the Royal Statistical Society Series B, 2007, vol. 69, issue 2, 163-183

Abstract: Summary. The paper considers Bayesian methods for density regression, allowing a random probability distribution to change flexibly with multiple predictors. The conditional response distribution is expressed as a non‐parametric mixture of regression models, with the mixture distribution changing with predictors. A class of weighted mixture of Dirichlet process 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 that are dependent on the distance between subjects’ predictor values. To allow local dependence in the mixture distributions, we propose a kernel‐based weighting scheme. A Gibbs sampling algorithm is developed for posterior computation. The methods are illustrated by using simulated data examples and an epidemiologic application.

Date: 2007
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