Dirichlet过程及非参数Bayes模型

Dirichlet process and Bayesian nonparametric models

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.