A predictive view of Bayesian clustering

This work considers probability models for partitions of a set of n elements using a predictive approach, i.e., models that are specified in terms of the conditional probability of either joining an already existing cluster or forming a new one. The inherent structure can be motivated by resorting to hierarchical models of either parametric or nonparametric nature. Parametric examples include the product partition models (PPMs) and the model-based approach of Dasgupta and Raftery (J. Amer. Statist. Assoc. 93 (1998) 294), while nonparametric alternatives include the Dirichlet process, and more generally, the species sampling models (SSMs). Under exchangeability, PPMs and SSMs induce the same type of partition structure. The methods are discussed in the context of outlier detection in normal linear regression models and of (univariate) density estimation.