Slice sampling σ-stable Poisson-Kingman mixture models

The paper is concerned with the use of Markov chain Monte Carlo methods for pos- terior sampling in Bayesian nonparametric mixture models. In particular we consider the problem of slice sampling mixture models for a large class of mixing measures generaliz- ing the celebrated Dirichlet process. Such a class of measures, known in the literature as σ-stable Poisson-Kingman models, includes as special cases most of the discrete priors currently known in Bayesian nonparametrics, e.g., the two parameter Poisson-Dirichlet process and the normalized generalized Gamma process. The proposed approach is illustrated on some simulated data examples.