The Annals of Statistics

Shrinkage priors for Bayesian prediction

Fumiyasu Komaki

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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.

Article information

Source
Ann. Statist., Volume 34, Number 2 (2006), 808-819.

Dates
First available in Project Euclid: 27 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1151418241

Digital Object Identifier
doi:10.1214/009053606000000010

Mathematical Reviews number (MathSciNet)
MR2283393

Zentralblatt MATH identifier
1092.62037

Subjects
Primary: 62F15: Bayesian inference 62C15: Admissibility

Keywords
Asymptotic theory conformal transformation information geometry Jeffreys prior Kullback–Leibler divergence vague prior

Citation

Komaki, Fumiyasu. Shrinkage priors for Bayesian prediction. Ann. Statist. 34 (2006), no. 2, 808--819. doi:10.1214/009053606000000010. https://projecteuclid.org/euclid.aos/1151418241


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