Species sampling priors for modeling dependence: An application to the detection of chromosomal aberrations

We discuss a class of Bayesian nonparametric priors that can be used to model local dependence in a sequence of observations.Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, common exchangeability assumptions may not be appropriate.We discuss a generalization of species sampling sequences, where the weights in the predictive probability functions are allowed to depend on a sequence of independent (not necessarily identically distributed) latent random variables. More specifically, we consider conditionally identically distributed (CID) Pitman-Yor sequences and the Beta-GOS sequences recently introduced by Airoldi et al. (Journal of the American Statistical Association, 109, 1466-1480, 2014). We show how those processes can be used as a prior distribution in a hierarchical Bayes modeling framework, and, in particular, how the Beta-GOS can provide a reasonable alternative to the use of non-homogenous Hidden Markov models, further allowing unsupervised clustering of the observations in an unknown number of states. The usefulness of the approach in biostatistical applications is discussed and explicitly shown for the detection of chromosomal aberrations in breast cancer.