Subhadip Pal, Ph.D., Department of Bioinformatics and Biostatistics, University of Louisville

"A Bayesian Framework for Modeling Data on the Stiefel Manifold"

A Bayesian framework 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, a family of conjugate priors, and an efficient Markov chain Monte Carlo (MCMC) sampling scheme for the corresponding posteriors is then developed for the posterior inference. Theoretical properties of the prior and posterior distributions are explored in detail. A novel procedure for efficient computation of a class of the hypergeometric function of a matrix argument is developed to facilitate the posterior inference. To showcase the methodology developed in this paper, we analyzed the vectorcardiogram dataset discussed in in Downs, Liebman and Mackay (1971).

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