Generalized Species Sampling Priors with Latent Beta reinforcements

TL;DR

This paper introduces a new family of non-exchangeable Bayesian nonparametric priors based on species sampling sequences with Beta reinforcements, offering more flexible modeling options beyond exchangeable assumptions.

Contribution

It develops a novel, probabilistically coherent class of non-exchangeable species sampling priors with tractable predictive functions and characterizes their joint process, extending existing models.

Findings

The new priors exhibit distinct clustering properties compared to Dirichlet and Poisson-Dirichlet processes.

Simulation studies show improved robustness and performance in hierarchical Bayesian models.

Application to breast cancer data demonstrates practical utility in detecting chromosomal aberrations.

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.