Bayesian density regression

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 predic...

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Veröffentlicht in:Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2007-04, Vol.69 (2), p.163-183
Hauptverfasser: Dunson, David B., Pillai, Natesh, Park, Ju-Hyun
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1369-7412
1467-9868
DOI:10.1111/j.1467-9868.2007.00582.x