On the stick-breaking representation of σ-stable Poisson-Kingman models

Abstract

In this paper we investigate the stick-breaking representation for the class of σ-stable Poisson-Kingman models, also known as Gibbs-type random probability measures. This class includes as special cases most of the discrete priors commonly used in Bayesian nonparametrics, such as the two parameter Poisson-Dirichlet process and the normalized generalized Gamma process. Under the assumption σ = u/v, for any coprime integers 1 ≤ u