Bayesian Nonparametric Analysis for a Generalized Dirichlet Process Prior

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• 作者：Antonio Lijoi ; Rams¨¦s H. Mena and Igor Pr¨¹nster
• 关键词：Bayesian nonparametric inference ; Dirichlet process ; generalized gamma convolutions ; Lauricella hypergeometric functions ; means of random probability measures ; predictive distributions
• 刊名：Statistical Inference for Stochastic Processes
• 出版年：2005
• 出版时间：December 2005
• 年：2005
• 卷：8
• 期：3
• 页码：283-309
• 全文大小：286 KB

文摘

This paper considers a generalization of the Dirichlet process which is obtained by suitably normalizing superposed independent gamma processes having increasing integer-valued scale parameter. A comprehensive treatment of this random probability measure is provided. We prove results concerning its finite-dimensional distributions, moments, predictive distributions and the distribution of its mean. Most expressions are given in terms of multiple hypergeometric functions, thus highlighting the interplay between Bayesian Nonparametrics and special functions. Finally, a suitable simulation algorithm is applied in order to compute quantities of statistical interest.