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Biometrika Advance Access originally published online on November 3, 2008
Biometrika 2008 95(4):859-874; doi:10.1093/biomet/asn043
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© 2008 Biometrika Trust

Articles

Bayesian nonparametric inference on stochastic ordering

David B. Dunson

Department of Statistical Science, Box 90251, Duke University, Durham, North Carolina 27708, U.S.A. dunson{at}stat.duke.edu

Shyamal D. Peddada

Biostatistics Branch, MD A3-03, National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709, U.S.A. peddada{at}niehs.nih.gov

Received for publication 1 January 2007. Revision received 1 February 2008.
  Abstract

We consider Bayesian inference about collections of unknown distributions subject to a partial stochastic ordering. To address problems in testing of equalities between groups and estimation of group-specific distributions, we propose classes of restricted dependent Dirichlet process priors. These priors have full support in the space of stochastically ordered distributions, and can be used for collections of unknown mixture distributions to obtain a flexible class of mixture models. Theoretical properties are discussed, efficient methods are developed for posterior computation using Markov chain Monte Carlo simulation and the methods are illustrated using data from a study of DNA damage and repair.

Key Words: Dependent Dirichlet process • Hypothesis testing • Mixture model • Nonparametric Bayes inference • Order restriction


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