Title: Bayesian model-based clustering with the telescoping sampler
Authors: Sylvia Fruehwirth-Schnatter - WU Vienna University of Economics and Business (Austria)
Gertraud Malsiner-Walli - WU Vienna University of Economics and Business (Austria)
Bettina Gruen - WU (Vienna University of Economics and Business) (Austria) [presenting]
Abstract: Mixtures of finite mixtures (MFM) are a suitable model class for model-based clustering in a Bayesian framework. In MFMs, a prior is also specified for the number of components in the finite mixture model to account for the uncertainty regarding the number of clusters. We discuss suitable prior specifications for the MFM model in model-based clustering applications as well as possible methods for inspecting implicitly induced prior distributions on the number of data clusters and partitions of the observations. Assuming that only a small number of data clusters are observed in the data set suggests using a dynamic specification of the weight prior where the gap between the number of components and the number of data clusters a-priori increases with an increasing number of components. For inference of the dynamic MFM, we propose to use the telescoping sampler, which extends the Markov chain Monte Carlo sampling scheme with data augmentation of the finite mixture model with a fixed number of components by sampling also from the posterior of the number of components. We will demonstrate the general applicability and performance of the telescoping sampler on mixture models with different component models.