The Annals of Statistics

Nonsubjective priors via predictive relative entropy regret

Trevor J. Sweeting, Gauri S. Datta, and Malay Ghosh

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Abstract

We explore the construction of nonsubjective prior distributions in Bayesian statistics via a posterior predictive relative entropy regret criterion. We carry out a minimax analysis based on a derived asymptotic predictive loss function and show that this approach to prior construction has a number of attractive features. The approach here differs from previous work that uses either prior or posterior relative entropy regret in that we consider predictive performance in relation to alternative nondegenerate prior distributions. The theory is illustrated with an analysis of some specific examples.

Article information

Source
Ann. Statist. Volume 34, Number 1 (2006), 441-468.

Dates
First available: 2 May 2006

Permanent link to this document
http://projecteuclid.org/euclid.aos/1146576270

Digital Object Identifier
doi:10.1214/009053605000000804

Mathematical Reviews number (MathSciNet)
MR2275249

Zentralblatt MATH identifier
05034318

Subjects
Primary: 62F15: Bayesian inference
Secondary: 62B10: Information-theoretic topics [See also 94A17] 62C20: Minimax procedures

Keywords
Nonsubjective Bayesian inference predictive inference relative entropy loss higher-order asymptotics

Citation

Sweeting, Trevor J.; Datta, Gauri S.; Ghosh, Malay. Nonsubjective priors via predictive relative entropy regret. The Annals of Statistics 34 (2006), no. 1, 441--468. doi:10.1214/009053605000000804. http://projecteuclid.org/euclid.aos/1146576270.


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