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Bayesian Density Regression

David B. Dunson, Natesh Pillai and Ju-Hyun Park
Journal of the Royal Statistical Society. Series B (Statistical Methodology)
Vol. 69, No. 2 (2007), pp. 163-183
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/4623261
Page Count: 21
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Bayesian Density Regression
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Abstract

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.

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