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 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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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. |
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ISSN: | 1369-7412 1467-9868 |
DOI: | 10.1111/j.1467-9868.2007.00582.x |