Bayesian Analysis

On the Support of MacEachern’s Dependent Dirichlet Processes and Extensions

Andrés F. Barrientos, Alejandro Jara, and Fernando A. Quintana

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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.

Article information

Source
Bayesian Anal., Volume 7, Number 2 (2012), 277-310.

Dates
First available in Project Euclid: 16 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1339878889

Digital Object Identifier
doi:10.1214/12-BA709

Mathematical Reviews number (MathSciNet)
MR2934952

Zentralblatt MATH identifier
1330.60067

Keywords
Related probability distributions Bayesian nonparametrics Copulas Weak support Hellinger support Kullback–Leibler support Stick–breaking processes

Citation

Barrientos, Andrés F.; Jara, Alejandro; Quintana, Fernando A. On the Support of MacEachern’s Dependent Dirichlet Processes and Extensions. Bayesian Anal. 7 (2012), no. 2, 277--310. doi:10.1214/12-BA709. https://projecteuclid.org/euclid.ba/1339878889


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