Bayesian predictive densities as an interpretation of a class of skew–student t distributions with application to medical data

Abstract

This paper describes a new Bayesian interpretation of a class of skew–Student t distributions. We consider a hierarchical normal model with unknown covariance matrix and show that by imposing different restrictions on the parameter space, corresponding Bayes predictive density estimators under Kullback-Leibler loss function embrace some well-known skew–Student t distributions. We show that obtained estimators perform better in terms of frequentist risk function over regular Bayes predictive density estimators. We apply our proposed methods to estimate future densities of medical data: the leg-length discrepancy and effect of exercise on the age at which a child starts to walk.