  Analysis of a Bayesian mixture model for the Matrix Langevin distribution on
the Stiefel manifold is presented. The model exploits a particular
parametrization of the Matrix Langevin distribution, various aspects of which
are elaborated on. A general, and novel, family of conjugate priors, and an
efficient Markov chain Monte Carlo (MCMC) sampling scheme for the corresponding
posteriors is then developed for the mixture model. Theoretical properties of
the prior and posterior distributions, including posterior consistency, are
explored in detail. Extensive simulation experiments are presented to validate
the efficacy of the framework. Real-world examples, including a large scale
neuroimaging dataset, are analyzed to demonstrate the computational
tractability of the approach.
