  We investigate Bayesian predictions for Wishart distributions by using the
Kullback-Leibler divergence. We compare between the Bayesian predictive
distributions based on a recently introduced class of prior distributions,
called the family of enriched standard conjugate priors, which includes the
Jeffreys prior, the reference prior, and the right invariant prior. We
explicitly calculate the risks of Bayesian predictive distributions without
using asymptotic expansions and clarify the dependency on the sizes of current
and future observations. We also construct a minimax predictive distribution
with a constant risk and prove this predictive distribution is not admissible.
