Dirichlet过程及非参数Bayes模型  

Dirichlet process and Bayesian nonparametric models

作　　者：张钧曦 胡耀忠 Junxi Zhang;Yaozhong Hu

机构地区：[1]Department of Mathematical and Statistical Sciences,University of Alberta at Edmonton,Alberta T6G 2G1,Canada

出　　处：《中国科学：数学》2021年第11期1895-1932,共38页Scientia Sinica：Mathematica

基　　金：Natural Sciences and Engineering Research Council of Canada(Grant No.RES0038963)资助项目。

摘　　要：自从Ferguson的里程碑式的工作以来,非参数Bayes模型在统计和机器学习等领域中有着广泛的应用,近年来得到了蓬勃的发展.它的一个重要的理论基础是一个特殊的随机概率测度族,即Dirichlet过程.本文介绍Dirichlet过程的构造、性质、推广以及它在非参数Bayes估计问题中的应用.另外,本文也提到双参数Poisson-Dirichlet过程、Beta过程和更一般的断棍(stick-breaking)过程以及相关性质.Bayesian nonparametric models have been extensively developed and widely used in statistics,machine learning and other areas since the ground breaking work of Ferguson.The fundamental of Bayesian nonparametric models is a special class of random probability measures:Dirichlet processes.This paper introduces the constructions,properties and some recent developments of the Dirichlet processes as well as their applications to Bayesian nonparametric estimation problems.We are also concerned with two-parameter Poisson-Dirichlet processes,Beta processes and more general stick-breaking processes and their properties.

关 键 词：Dirichlet过程 断棍过程 双参数Poisson-Dirichlet过程 POISSON过程 中国餐馆模型 印度自助餐模 型 非参数Bayes模型 U-统计量 

分 类 号：O212.8[理学—概率论与数理统计]