title: 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 non-exchangeable 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 Processes mixtures and Hidden Markov Models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array CGH data.
authors: Department of Statistics at Harvard University and an Alfred P. Sloan Research Fellow.
authors: Edoardo M
authors: EM
authors: Airoldi
authors: School of Engineering and Applied Sciences at Harvard University.
authors: Thiago
authors: T
authors: Costa
authors: Department of Mathematics at Universita di Pavia, Italy.
authors: Federico
authors: F
authors: Bassetti
authors: Department of Statistics at University of Kent, UK.
authors: Fabrizio
authors: F
authors: Leisen
authors: Department of Biostatistics at MD Anderson Cancer Center.
authors: Michele
authors: M
authors: Guindani
keywords: Bayesian non-parametrics; Cancer; Genomics; MCMC; Predictive Probability Functions; Random Partitions; Species Sampling Priors