Shrinkage priors for Bayesian prediction

Abstract

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.

Published at http://dx.doi.org/10.1214/009053606000000010 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Improved minimax predictive densities under Kullback--Leibler loss
• Shrinkage priors for Bayesian prediction

Cited by in corpus (3)

• Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models
• Shrinkage priors for Bayesian prediction
• Bayesian shrinkage prediction for the regression problem