Recent advances on overfitting Bayesian mixture models provide a solid andstraightforward approach for inferring the underlying number of clusters andmodel parameters in heterogeneous data. In this study we demonstrate theapplicability of such a framework in clustering multivariate continuous datawith possibly complex covariance structure. For this purpose an overfittingmixture of factor analyzers is introduced, assuming that the number of factorsis fixed. A Markov chain Monte Carlo (MCMC) sampler combined with a priorparallel tempering scheme is used to estimate the posterior distribution ofmodel parameters. The optimal number of factors is estimated using informationcriteria. Identifiability issues related to the label switching problem aredealt by post-processing the simulated MCMC sample by relabelling algorithms.The method is benchmarked against state-of-the-art software for maximumlikelihood estimation of mixtures of factor analyzers and standard mixtures ofmultivariate Gaussian distributions using an extensive simulation study.Finally, the applicability of the method is illustrated in publicly availabledata.
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