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

By Andrés F. Barrientos, Alejandro Jara, Fernando A. Quintana. 2012

95 citations recorded by the source corpus.

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 deflnition of MacEachern's dependent Dirichlet processes. Based on this deflnition, we provide su-cient conditions for the full weak support of difierent 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 difierent versions of the dependent Dirichlet process. A generalization of the results for the general class of dependent stick{ breaking processes is also provided.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a73f0162220b428fd576361d1f693a759868968c

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Citations in the corpus

Bayesian inference with dependent normalized completely random measures (2014, background): “One of the main reasons of the success of stick-breaking constructions is their attractiveness from computational point of view along with their flexibility since, as shown in [3], they have full weak support under mild assumptions.”