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:IEEE transactions on information theory 2019-09, Vol.65 (9), p.5352-5366
Main Authors: Maruyama, Yuzo, Matsuda, Takeru, Ohnishi, Toshio
Format: Article
Language:English
Subjects:
Bayes methods
Bayesian predictive density
Covariance matrices
Estimation
Harmonic analysis
harmonic prior
Indexes
minimaxity
Predictive models
Robustness
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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 or equal to 3. Alpha divergence from the true distribution to a predictive distribution is adopted as a loss function.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2019.2915245