Bayesian analysis of multivariate mixture models via factor analyzer

Abstract

We consider a new Bayesian finite mixture model for multivariate data. A problem is to estimate the covariance matrix since the number of parameters for the covariance matrix is squarely proportional to the dimension of data. Also, the inverting large dimensional covariate, which is necessary for MCMC algorithms, is very time consuming and practically almost prohibited. In this thesis, we propose a way of reducing the parameters in the covariance matrices by use of the factor model. That is, the dependence structure of each component is assumed to be represented by linear combinations of factors. To simply the model and improve interpretability further, we allow some factors can be shared across the components. From numerical studies, we confirmed that our method well perform with different component covariance structure.