  We investigate shrinkage priors for constructing Bayesian predictive
distributions. It is shown that there exist shrinkage predictive distributions
asymptotically dominating Bayesian predictive distributions based on the
Jeffreys prior or other vague priors if the model manifold satisfies some
differential geometric conditions. Kullback--Leibler divergence from the true
distribution to a predictive distribution is adopted as a loss function.
Conformal transformations of model manifolds corresponding to vague priors are
introduced. We show several examples where shrinkage predictive distributions
dominate Bayesian predictive distributions based on vague priors.
