Subjective Bayesian Analysis of the Elliptical Model

For the multivariate elliptical model subjective Bayesian estimators of the location vector and some functions of the characteristic matrix with the normal-inverse Wishart and the normal-Wishart as prior, respectively, are derived. Fang and Li (1999 Fang, K.T., Li, R.Z. (1999). Bayesian statistical inference on elliptical matrix distributions. J. Multivariate Anal. 70: 66–85.[Crossref], [Web of Science ®] , [Google Scholar]) considered the elliptical model for Bayesian analysis for an objective prior structure. In addition, the newly developed results are applied to the multivariate normal- and t-distribution. A performance study is done to evaluate the normal-gamma and normal-inverse gamma distributions as suitable priors. A practical application for the posterior distributions of the multivariate t-distribution is included by means of Gibbs sampling and a Metropolis-Hastings algorithm.