On the support of maceachern's dependent dirichlet processes and extensions
| Autor: | Alejandro Jara, Andrés F. Barrientos, Fernando A. Quintana |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Statistics and Probability
Hierarchical Dirichlet process Statistics::Theory Kullback–Leibler support Weak support Stochastic process Related probability distributions Applied Mathematics Copula (linguistics) Stick–breaking processes Dependent Dirichlet process Dirichlet distribution Dirichlet process Bayesian nonparametrics symbols.namesake Generalized Dirichlet distribution Econometrics symbols Probability distribution Applied mathematics Statistics::Methodology Copulas Hellinger support Mathematics |
| Zdroj: | BAYESIAN ANALYSIS Artículos CONICYT CONICYT Chile instacron:CONICYT Bayesian Anal. 7, no. 2 (2012), 277-310 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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