A Bayesian Analysis of Hierarchical Mixtures with Application to Clustering Fingerprints

Hierarchical mixture models arise naturally for clustering a heterogeneous population of objects where observations made on each object follow a standard mixture density. Hierarchical mixtures utilize complementary aspects of mixtures at different levels of the hierarchy. At the first (top) level, the mixture is used to perform clustering of the objects, while at the second level, nested mixture models are used as flexible representations of distributions of observables from each object. Inference for hierarchical mixtures is more challenging since the number of unknown mixture components arise in both the first and second levels of the hierarchy. In this paper, a Bayesian approach based on Reversible Jump Markov Chain Monte Carlo methodology is developed for the inference of all unknown parameters of hierarchical mixtures. Our methodology is then applied to the clustering of fingerprint images and used to assess the variability of quantities which are functions of the second level mixtures.