A Bayesian approach to cluster analysis

Abstract

A general probabilistic model for describing the structure of statistical problems known under the generic name of cluster analysis, based on finite mixtures of distributions, is proposed. We analyse the theoretical and practical implications of this approach, and point out some open question on both the theoretical problem of determining the reference prior for models based on mixtures, and the practical problem of approximation that mixtures typically entail. Finally, models based on mixtures of normal distributions are analised with some detail.