Generalized Species Sampling Priors with Latent Beta reinforcements

Many popular Bayesian Nonparametric priors can be characterized in terms of exchangeable species sampling sequences. One example is the Dirichlet Process prior, that has been increasingly used for modeling purposes in mixture of DP hierarchical models. However, in some applications, the implied exchangeability assumption may not be considered appropriate. We introduce non exchangeable generalized species sampling priors characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We discuss some of the properties that can be useful in applications, and we compare our findings with well-known properties of the DP and the two parameters Poisson-Dirichlet process. We detail on Markov Chain Monte Carlo posterior sampling, and illustrate the behavior of such priors by means of a simulation study and an application to the detection of chromosomal aberrations in breast cancer using array CGH data.