Generalized Species Sampling Priors With Latent Beta Reinforcements

• 成果类型: Article
• 署名作者: Airoldi, Edoardo M.; Costa, Thiago; Bassetti, Federico; Leisen, Fabrizio; Guindani, Michele
• 署名单位: Harvard University; Harvard University; University of Pavia; University of Kent; University of Texas System; UTMD Anderson Cancer Center
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.950735
• 发表日期: 2014
• 页码: 1466-1480
• 关键词: hidden-markov model; nonparametric bayesian models; partition models; mixture; aberrations; selection

摘要

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.