Abstract:
In this paper, we consider a general framework for constructing new valid densities
regarding a random matrix variate. However, we focus speci cally on the Wishart
distribution. The methodology involves coupling the density function of the Wishart
distribution with a Borel measurable function as a weight. We propose three di erent
weights by considering trace and determinant operators on matrices. The charac-
teristics for the proposed weighted-type Wishart distributions are studied and the
enrichment of this approach is illustrated. A special case of this weighted-type dis-
tribution is applied in the Bayesian analysis of the normal model in the univariate
and multivariate cases. It is shown that the performance of this new prior model is
competitive using various measures.
