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Shrinkage priors for Bayesian prediction. (English) Zbl 1092.62037

Summary: 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.

MSC:

62F15 Bayesian inference
62C15 Admissibility in statistical decision theory
53B21 Methods of local Riemannian geometry
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