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Bayesian density regression


  • David B. Dunson
  • Natesh Pillai
  • Ju‐Hyun Park


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.

Suggested Citation

  • David B. Dunson & Natesh Pillai & Ju‐Hyun Park, 2007. "Bayesian density regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 163-183, April.
  • Handle: RePEc:bla:jorssb:v:69:y:2007:i:2:p:163-183
    DOI: 10.1111/j.1467-9868.2007.00582.x

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