NSF-CBMS Regional Conference Series in Probability and Statistics, Volume 9
“Nonparametric Bayesian Inference”
by Peter Müller and Abel Rodriguez

The notes provide an overview of some popular Bayesian nonparametric (BNP) probability models. The discussion follows a logical development of many commonly used nonparametric Bayesian models as generalizations of the Dirichlet process (DP) in different directions, including Pólya tree (PT) models, species sampling models (SSM), dependent DP (DDP) models and product partition models (PPM). The selection of topics is subjective, simply driven by what the authors are familiar with. As a result, some useful and elegant classes of models such as normalized random measures with random increments (NRMIs) are reviewed only briefly.