On a class of multivariate normal selection priors and its applications in Bayesian inference

This paper suggests a new class of multivariate distributions useful for specifying flexible conjugate priors of normal mean vector. The distributions are obtained from weighting the multivariate normal distribution via conditioning method. The salient features of the class is mathematical tractability, distributional flexibility (strict inclusion of normal and skew-normal distributions), and capability of eliciting uncertainty about inequality constrained parameters in normal models. A stochastic representation, moments, and distributional properties of the class are studied with special emphasis on their closure properties. These developments are followed by Bayesian applications to normal models. The Markov chain Monte Carlo method is considered for estimating the models. Necessary theories and three practical applications demonstrating the utility of the class are provided.