Bayesian variable selection in clustering high-dimensional data

Over the last decade, technological advances have generated an explosion of data with substantially smaller sample size relative to the number of covariates (p [much greater than] n). A common goal in the analysis of such data involves uncovering the group structure of the observations and identifying the discriminating variables. In this article we propose a methodology for addressing these problems simultaneously. Given a set of variables, we formulate the clustering problem in terms of a multivariate normal mixture model with an unknown number of components and use the reversible-jump Markov chain Monte Carlo technique to define a sampler that moves between different dimensional spaces. We handle the problem of selecting a few predictors among the prohibitively vast number of variable subsets by introducing a binary exclusion/inclusion latent vector, which gets updated via stochastic search techniques. We specify conjugate priors and exploit the conjugacy by integrating out some of the parameters. We describe strategies for posterior inference and explore the performance of the methodology with simulated and real datasets. KEY WORDS: Bayesian variable selection; Bayesian clustering; Label switching; Reversible-jump Markov chain Monte Carlo.