  Finite mixtures of matrix normal distributions are a powerful tool for
classifying three-way data in unsupervised problems. The distribution of each
component is assumed to be a matrix variate normal density. The mixture model
can be estimated through the EM algorithm under the assumption that the number
of components is known and fixed. In this work we introduce, develop and
explore a Bayesian analysis of the model in order to provide a tool for
simultaneous model estimation and model selection. The effectiveness of the
proposed method is illustrated on a simulation study and on a real example.
