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June 2012 On the Support of MacEachern’s Dependent Dirichlet Processes and Extensions
Andrés F. Barrientos, Alejandro Jara, Fernando A. Quintana
Bayesian Anal. 7(2): 277-310 (June 2012). DOI: 10.1214/12-BA709

Abstract

We study the support properties of Dirichlet process–based models for sets of predictor–dependent probability distributions. Exploiting the connection between copulas and stochastic processes, we provide an alternative definition of MacEachern’s dependent Dirichlet processes. Based on this definition, we provide sufficient conditions for the full weak support of different versions of the process. In particular, we show that under mild conditions on the copula functions, the version where only the support points or the weights are dependent on predictors have full weak support. In addition, we also characterize the Hellinger and Kullback–Leibler support of mixtures induced by the different versions of the dependent Dirichlet process. A generalization of the results for the general class of dependent stick–breaking processes is also provided.

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Andrés F. Barrientos. Alejandro Jara. Fernando A. Quintana. "On the Support of MacEachern’s Dependent Dirichlet Processes and Extensions." Bayesian Anal. 7 (2) 277 - 310, June 2012. https://doi.org/10.1214/12-BA709

Information

Published: June 2012
First available in Project Euclid: 16 June 2012

zbMATH: 1330.60067
MathSciNet: MR2934952
Digital Object Identifier: 10.1214/12-BA709

Keywords: Bayesian nonparametrics , copulas , Hellinger support , Kullback–Leibler support , Related probability distributions , Stick–breaking processes , Weak support

Rights: Copyright © 2012 International Society for Bayesian Analysis

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Vol.7 • No. 2 • June 2012
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