Harmonic Bayesian prediction under alpha-divergence

We investigate Bayesian shrinkage methods for constructing predictive distributions. We consider the multivariate Normal model with a known covariance matrix and show that the Bayesian predictive density with respect to Stein's harmonic prior dominates the best invariant Bayesian predictive den...

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Bibliographic Details
Published in:arXiv.org 2017-07
Main Authors: Maruyama, Yuzo, Ohnishi, Toshio
Format: Article
Language:English
Subjects:
Bayesian analysis
Covariance matrix
Density
Divergence
Predictions
Shrinkage
Online Access:Get full text
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Summary:We investigate Bayesian shrinkage methods for constructing predictive distributions. We consider the multivariate Normal model with a known covariance matrix and show that the Bayesian predictive density with respect to Stein's harmonic prior dominates the best invariant Bayesian predictive density, when the dimension is greater than three. Alpha-divergence from the true distribution to a predictive distribution is adopted as a loss function.
ISSN:2331-8422