Generalized Species Sampling Priors With Latent Beta Reinforcements

Abstract

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 a novel and probabilistically coherent family of nonexchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet process and the two parameters Poisson–Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes’ modeling framework, and we describe a Markov chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet process mixtures and hidden Markov models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array comparative genomic hybridization (CGH) data. Supplementary materials for this article are available online.

• Bayesian nonparametrics
• Cancer
• Genomics
• MCMC
• Predictive probability functions
• Random partitions

SUPPLEMENTARY MATERIALS

The online supplementary materials contain additional results for various models discussed throughout the article.