Nonsubjective priors via predictive relative entropy regret

Details Nonsubjective priors via predictive relative entropy regret Nonsubjective priors via predictive relative entropy regret

2006-05-23

arxiv.org/abs/math/0605609v1

Annals of Statistics 2006, Vol. 34, No. 1, 441-468

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000804 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000804

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.

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