Mixtures of multivariate restricted skew-normal factor analyzer models in a Bayesian framework
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The mixture of factor analyzers (MFA) model, by reducing the number of free parameters through its factor-analytic representation of the component covariance matrices, is an important statistical model to identify hidden or latent groups in high dimensional data. Recent approaches to extend the approach to skewed data or skewness in the latent groups have been examined in a frequentist setting where there are some known computational limitations. For these reasons we consider a Bayesian approach to the restricted skew-normal mixtures of factor analysis MFA model. We examine the performance and flexibility of the approach on real datasets and illustrate some of the computational advantages in a missing data setting.
KeywordsBayesian analysis Gibbs sampling Mixture of factor analysis model Restricted skew-normal distribution
The authors would like to thank the associated editor and anonymous reviewers for their suggestions, corrections and encouragement, which helped us to improve earlier versions of the manuscript. We also would like to acknowledge helpful discussions with Geoff McLachlan and Sharon Lee (UQ) in the preparation of this work.
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