Dirichlet process and its developments: a survey

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.