Generalized Species Sampling Priors with Latent Beta reinforcements

Many popular Bayesian Nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce non exchangeable generalized species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their clustering properties with those of the Dirichlet Process and the two parameters Poisson-Dirichlet process. We propose the use of such sequences as prior distributions in a hierarchical Bayes modeling framework. We detail on Markov Chain Monte Carlo posterior sampling and discuss the resulting inference in a simulation study, comparing their performance with that of popular Dirichlet Processes mixtures and Hidden Markov Models. Finally, we discuss an application to the detection of chromosomal aberrations in breast cancer using array CGH data.