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 Jg. 69; H. 2; S. 163 - 183
Hauptverfasser:	Dunson, David B., Pillai, Natesh, Park, Ju-Hyun
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Oxford, UK Blackwell Publishing Ltd 01.04.2007 Blackwell Publishers Blackwell Royal Statistical Society Oxford University Press
Schriftenreihe:	Journal of the Royal Statistical Society Series B
Schlagworte:	algorithms Atoms Bayesian analysis Bayesian method Body mass index Computation Conditional density function Density Density estimation Dirichlet process Distribution Economic models Epidemiology Exact sciences and technology Generalized Pólya urn Linear inference, regression Linear regression Local smoothing Mathematical methods Mathematics Matrices Mixture model Modeling Nonparametric Bayes method Nonparametric inference Nonparametric models Obesity Parametric models Probability Probability and statistics probability distribution Regression analysis Sampling Sciences and techniques of general use Specification Statistical methods Statistics Studies Weighting Conditional density function Conditional distribution Prior distribution Mixture model Non parametric estimation Dirichlet process Gibbs sampling Algorithm Epidemiology Statistical method Generalized Pólya urn Probability density Nonparametric Bayes method Smoothing Regression model Mixed model Density function Bayes methods Posterior distribution Local smoothing
ISSN:	1369-7412, 1467-9868
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.
Bibliographie:	ArticleID:RSSB582 ark:/67375/WNG-DXRGW1V3-8 istex:C2C1437ED99BF758140106FD47F4B33C65C90234 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 ObjectType-Article-1 ObjectType-Feature-2
ISSN:	1369-7412 1467-9868
DOI:	10.1111/j.1467-9868.2007.00582.x