  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.
