Title: Generalized mixtures of finite mixtures
Authors: Gertraud Malsiner-Walli - WU Vienna University of Economics and Business (Austria) [presenting]
Sylvia Fruehwirth-Schnatter - WU Vienna University of Economics and Business (Austria)
Bettina Gruen - Wirtschaftsuniversität Wien (Austria)
Abstract: Within a Bayesian framework, an investigation of the model class of mixtures of finite mixtures (MFMs) where a prior on the number of components is specified is performed. This model class requires suitable prior specifications and inference methods to exploit its full potential. We contribute to the Bayesian analysis of MFMs by considering a generalized class of MFMs containing static and dynamic MFMs where the Dirichlet parameter of the component weights either is fixed or depends on the number of components. We emphasize the distinction between the number of components $K$ of a mixture and the number of clusters $K+$, i.e., the number of filled components. In the MFM model, $K+$ is a random variable, and its prior depends on the prior on the number of components $K$ and the mixture weights. We characterize the prior on the number of clusters $K+$ and derive computationally feasible formulas to calculate this implicit prior. For posterior inference, we propose the telescoping sampler, which allows Bayesian inference for mixtures with arbitrary component distributions. The telescoping sampler explicitly samples the number of components, but otherwise requires only the usual MCMC steps for estimating a finite mixture model. The ease of its application is demonstrated on a real data set.