Theory and computations for the Dirichlet process and related models: An overview

Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility and robustness against mis-specification of the probability model. In the Bayesian context, this is accomplished by placing a prior distribution on an infinite-dimensional space, referred to as Bayesian nonparametric models. We provide an overview on the most popular Bayesian nonparametric models for probability distributions and for collections of predictor-dependent probability distributions. The intention of is not to be complete or exhaustive, but rather to touch on areas of interest for the practical use of the priors in the context of a hierarchical model. We give an overview covering the main properties of the basic models and the algorithms for fitting them.