On the matrix-variate generalized hyperbolic distribution and its Bayesian applications

Abstract

Abstract In the first part of the paper, we introduce the matrix-variate generalized hyperbolic distribution by mixing the matrix normal distribution with the matrix generalized inverse Gaussian density. The p-dimensional generalized hyperbolic distribution of [Barndorff-Nielsen, O. (1978). Hyperbolic distributions and distributions on hyperbolae. Scand. J. Stat., 5, 151–157], the matrix-T distribution and many well-known distributions are shown to be special cases of the new distribution. Some properties of the distribution are also studied. The second part of the paper deals with the application of the distribution in the Bayesian analysis of the normal multivariate linear model. Keywords: Matrix-variate generalized hyperbolic distributionMatrix normal distributionMatrix generalized inverse Gaussian distributionNormal multivariate linear modelPosterior and prediction distributions Acknowledgements The research was supported in part by the Natural Science and Engineering Research Council of Canada. Thanks to the referee and editor for valuable comments.