Identifying Mixtures of Mixtures Using Bayesian Estimation

• Activity Number: 217 - Computing Making Impact: The Best of JCGS
• Type: Invited
• Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
• Sponsor: JCGS-Journal of Computational and Graphical Statistics
• Author(s): Bettina Grün* and Gertraud Malsiner-Walli and Sylvia Frühwirth-Schnatter
• Companies: Johannes Kepler Universität and Wirtschaftsuniversität Wien and Wirtschaftsuniversität Wien
• Keywords: model-based clustering; finite mixture model; number of components; hierarchical prior; MCMC

Abstract

Finite mixture models enable the approximation of data distributions in a semi-parametric way and the identification of groups in data. The mixture of mixtures approach uses a two-level model exploiting both. On the lower level mixtures approximate the cluster distribution and on the upper level mixtures group the data. Identifying the clusters in this setting is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework, we propose a different approach based on sparse finite mixtures. We specify a hierarchical prior with carefully selected hyperparameters to reflect the cluster structure aimed at and which enables model estimation using standard MCMC sampling methods. In combination with a post-processing approach to resolve the label switching issue, our approach allows us to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semi-parametric way and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in simulation studies and applications.