Shrinkage priors for Bayesian prediction

The Annals of Statistics · 2006 · Volume 34 · Issue 2

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.

Keywords

62C15, 62F15, Asymptotic theory, conformal transformation, information geometry, Jeffreys prior, Kullback–Leibler divergence, vague prior

Enable JavaScript for citation tools and additional paper interactions.