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Biometrika Advance Access originally published online on April 30, 2008
Biometrika 2008 95(2):307-323; doi:10.1093/biomet/asn012
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© US Government/Department of Health and Human Services 2008; Published by the Biometrika Trust

Articles

Kernel stick-breaking processes

David B. Dunson

Biostatistics Branch, National Institute of Environmental Health Sciences, P.O. Box 12233, Research Triangle Park, North Carolina 27709, U.S.A. dunson1{at}niehs.nih.gov

Ju-Hyun Park

Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A. parkj3{at}niehs.nih.gov

Received for publication 1 November 2006. Revision received 1 August 2007.
  Abstract

We propose a class of kernel stick-breaking processes for uncountable collections of dependent random probability measures. The process is constructed by first introducing an infinite sequence of random locations. Independent random probability measures and beta-distributed random weights are assigned to each location. Predictor-dependent random probability measures are then constructed by mixing over the locations, with stick-breaking probabilities expressed as a kernel multiplied by the beta weights. Some theoretical properties of the process are described, including a covariate-dependent prediction rule. A retrospective Markov chain Monte Carlo algorithm is developed for posterior computation, and the methods are illustrated using a simulated example and an epidemiological application.

Key Words: Conditional density estimation • Dependent Dirichlet process • Kernel methods • Nonparametric Bayes • Mixture model • Prediction rule • Random partition


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