  We investigate Bayesian shrinkage methods for constructing predictive
distributions. We consider the multivariate Normal model with a known
covariance matrix and show that the Bayesian predictive density with respect to
Stein's harmonic prior dominates the best invariant Bayesian predictive
density, when the dimension is greater than three. Alpha-divergence from the
true distribution to a predictive distribution is adopted as a loss function.
