Title: Reliable variance matrix priors for Bayesian mixture models with Gaussian kernels
Authors: Michail Papathomas - University of St Andrews (United Kingdom) [presenting]
Wei Jing - University of St Andrews (United Kingdom)
Silvia Liverani - Queen Mary University of London (United Kingdom)
Abstract: Bayesian mixture modelling is an increasingly popular approach for clustering and density estimation. We study the choice of prior for the variance or precision matrix when Gaussian kernels are adopted. Typically, mixture models are assessed by considering observations in the space of only a handful of dimensions. Instead, we are concerned with higher dimensionality problems, in the space of up to 20 dimensions, observing that the choice of prior becomes increasingly important as the dimensionality increases. After identifying certain undesirable properties of standard priors, we review and implement possible alternative priors. The most promising priors are identified, as well as factors that affect MCMC convergence. Results, using simulated and real data, show that the choice of prior and its implementation are critical for deriving reliable inferences. The focus is on the Dirichlet Process Mixture Model, but we also discuss its relevance to Bayesian Mixtures of Finite Mixture models.