## Bayesian density regression (2007)

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Venue: | JOURNAL OF THE ROYAL STATISTICAL SOCIETY B |

Citations: | 40 - 23 self |

### BibTeX

@ARTICLE{Dunson07bayesiandensity,

author = {David B. Dunson and Natesh Pillai},

title = {Bayesian density regression},

journal = {JOURNAL OF THE ROYAL STATISTICAL SOCIETY B},

year = {2007},

volume = {69},

pages = {163--183}

}

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### Abstract

This article considers Bayesian methods for density regression, allowing a random probability distribution to change flexibly with multiple predictors. The conditional response dis-tribution is expressed as a nonparametric mixture of parametric densities, with the mixture distri-bution changing according to location in the predictor space. A new class of priors for dependent random measures is proposed for the collection of random mixing measures at each location. The conditional prior for the random measure at a given location is expressed as a mixture of a Dirichlet process (DP) distributed innovation measure and neighboring random measures. This specifica-tion results in a coherent prior for the joint measure, with the marginal random measure at each location being a finite mixture of DP basis measures. Integrating out the infinite-dimensional col-lection of mixing measures, we obtain a simple expression for the conditional distribution of the subject-specific random variables, which generalizes the Pólya urn scheme. Properties are consid-ered and a simple Gibbs sampling algorithm is developed for posterior computation. The methods are illustrated using simulated data examples and epidemiologic studies.

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Citation Context ...s Gx indexed by a vector x ∈ XD of categorical covariates. In particular, they defined a prior for the array of random measures 2sGX = {Gx, x ∈ XD}, which maintains a marginal Dirichlet process (DP) (=-=Ferguson, 1973-=-; 1974) structure for the distribution at each value of x. This is accomplished using the dependent Dirichlet process (DDP) approach of MacEachern (1999; 2000; 2001), which relies on expressing the DP... |

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Citation Context ... distribution at each value of x. This is accomplished using the dependent Dirichlet process (DDP) approach of MacEachern (1999; 2000; 2001), which relies on expressing the DP in stick-breaking form (=-=Sethuraman, 1994-=-): Gx = ∞� h=1 πx,hδθx,h , with πx,h/ �h−1 iid l=1 (1 − πx,l) ∼ beta(1, α), where {πx,h} are random weights, δθ is a degenerate distribution with all its mass at θ, and {θx,h} are atoms generated from... |

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