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Title: Inferring components and clusters in Bayesian finite mixture modelling Authors:  Sylvia Fruhwirth-Schnatter - WU Vienna (Austria)
Bettina Gruen - Wirtschaftsuniversität Wien (Austria)
Gertraud Malsiner-Walli - WU Vienna University of Business and Economics (Austria) [presenting]
Abstract: The selection of a suitable number of mixture components is a difficult problem in finite mixture modelling without a generally accepted solution so far. The choice of the number of mixture components is in general crucial, because it is assumed that each mixture component captures exactly one data cluster. In the Bayesian framework, a natural approach to estimate the number of components is to treat it as an unknown model parameter, specify a prior on it and determine its posterior distribution. Several inference methods have been proposed for estimating this distribution, in particular, reversible jump Markov chain Monte Carlo (RJMCMC) techniques. However, it can be a difficult task to design suitable proposal densities in higher-dimensional parameter spaces for these samplers. Based on recently published results, we propose an alternative approach where we distinguish between the total number of mixture components in the mixture model and the number of `active' components, i.e. components, to which observations are assigned and which correspond to the data clusters. In this way we are able to make inference on both the number of mixture components and the number of data clusters without employing complex transdimensional sampling techniques, but rather using only familiar Gibbs sampling techniques. This approach is illustrated using simulation studies and real applications.