Distributions of linear functionals of two parameter Poisson-Dirichlet random measures

• 成果类型: Article
• 署名作者: James, Lancelot F.; Lijoi, Antonio; Prunster, Igor
• 署名单位: Hong Kong University of Science & Technology; University of Pavia; University of Turin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP462
• 发表日期: 2008
• 页码: 521-551
• 关键词: stable subordinator; partitions; priors

摘要

The present paper provides exact expressions for the probability distributions of linear functionals of the two-parameter Poisson-Dirichlet process PD(alpha, theta). We obtain distributional results yielding exact forms for density functions of these functionals. Moreover, several interesting integral identities are obtained by exploiting a correspondence between the mean of a Poisson-Dirichlet process and the mean of a suitable Dirichlet process. Finally, some distributional characterizations in terms of mixture representations are proved. The usefulness of the results contained in the paper is demonstrated by means of some illustrative examples. Indeed, our formulae are relevant to occupation time phenomena connected with Brownian motion and more general Bessel processes, as well as to models arising in Bayesian nonparametric statistics.