Abstract

Infinite mixture models reposed on random probability measures like the Dirichlet process allow for flexible modelling of densities and for clustering applications where the number of clusters is not fixed a priori. This is because we can formulate the problem as a hierarchical model where the top level is a (discrete) random probability measure. In recent years, there has been a growing interest in using other random probability measures, beyond the classical Dirichlet process, for extending modelling flexibility . Examples include Pitman-Yor processes, normalized inverse Gaussian processes, and normalized random measures. Our understanding of these models has grown significantly over the last decade: there is an increasing realisation that while these models are nonparametric in nature and allow an arbitrary number of components to be used, they do impose significant prior assumptions regarding the clustering structure.

In this talk I will present a very wide class of random probability measures, called σ-stable Poisson-Kingman processes, and discuss its use for Bayesian nonparametric mixture modelling. This class of processes encompasses most known random probability measures proposed in the literature so far, and we argue that it forms a natural class to study. I will review certain characterisations which lead us to propose a tractable and exact posterior inference algorithm for the whole class.

This is joint work with Yee Whye Teh and Stefano Favaro. The talk is based on our preprint.