Dirichlet process and its developments: a survey  

作　　者：Yemao XIA Yingan LIU Jianwei GOU 

机构地区：[1]School of Sciences,Nanjing Forestry University,Nanjing 210037,China [2]College of Information Science and Technology,Nanjing Forestry University,Nanjing 210037,China

出　　处：《Frontiers of Mathematics in China》2022年第1期79-115,共37页中国高等学校学术文摘·数学（英文）

基　　金：supported in part by the National Natural Science Foundation of China(Grant No.11471161);the Technological Innovation Item in Jiangsu Province(No.BK2008156).

摘　　要：The core of the nonparametric/semiparametric Bayesian analysis is to relax the particular parametric assumptions on the distributions of interest to be unknown and random,and assign them a prior.Selecting a suitable prior therefore is especially critical in the nonparametric Bayesian fitting.As the distribution of distribution,Dirichlet process(DP)is the most appreciated nonparametric prior due to its nice theoretical proprieties,modeling flexibility and computational feasibility.In this paper,we review and summarize some developments of DP during the past decades.Our focus is mainly concentrated upon its theoretical properties,various extensions,statistical modeling and applications to the latent variable models.

关 键 词：Nonparametric Bayes Dirichlet process Polya urn prediction Sethuraman representation stick-breaking procedure Chinese restaurant rule mixture of Dirichlet process dependence Dirichlet process Markov Chains Monte Carlo blocked Gibbs sampler latent variable models 

分 类 号：O17[理学—数学]