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Bayesian density regression
Author(s) -
Dunson David B.,
Pillai Natesh,
Park JuHyun
Publication year - 2007
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00582.x
Subject(s) - mathematics , gibbs sampling , dirichlet process , dirichlet distribution , bayesian linear regression , conditional probability distribution , prior probability , kernel (algebra) , posterior probability , statistics , kernel regression , mixture model , bayesian probability , kernel density estimation , regression , bayesian inference , discrete mathematics , mathematical analysis , estimator , boundary value problem
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.