文章基本信息

标题：Stochastic Approximations to the Pitman–Yor Process
本地全文：下载
作者：Julyan Arbel ; Pierpaolo De Blasi ; Igor Prünster 等
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2019
卷号：14
期号：4
页码：1201-1219
DOI：10.1214/18-BA1127
语种：English
出版社：International Society for Bayesian Analysis
摘要：In this paper we consider approximations to the popular Pitman–Yor process obtained by truncating the stick-breaking representation. The truncation is determined by a random stopping rule that achieves an almost sure control on the approximation error in total variation distance. We derive the asymptotic distribution of the random truncation point as the approximation error ? goes to zero in terms of a polynomially tilted positive stable random variable. The practical usefulness and effectiveness of this theoretical result is demonstrated by devising a sampling algorithm to approximate functionals of the ? -version of the Pitman–Yor process.
关键词：stochastic approximation; asymptotic distribution; Bayesian Nonparametrics; Pitman–Yor process; random functionals; random probability measure; stopping rule.