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Bayesian density regression
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DOI：10.1111/j.1467-9868.2007.00582.x.png)
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Abstract
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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 Polya 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.
Keywords:
conditional density function
Dirichlet process
generalized Polya um
local smoothing
mixture model
monparametric Bayes method
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