Shannon optimal priors on independent identically distributed statistical experiments converge weakly to Jeffreys' prior
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- 作者：Holger R. Scholl (1)
- 关键词：Key Words Bayes risk ; channel capacity ; Jeffreys' prior ; Kullback ; Leibler distance ; minimax risk ; noninformative prior ; reference prior ; Shannon optimal prior ; statistical experiment
- 刊名：TEST
- 出版时间：June 1998
- 出版年：1998
- 期刊代码：pc625_1133-0686
- 类别：mat
- 卷：7
- 期：1
- 页码：75-94
- 数据来源：sp
摘要
In 1979, J.M. Bernardo argued heuristically that in the case of regular product experiments his information theoretic reference prior is equal to Jeffreys' prior. In this context, B.S. Clarke and A.R. Barron showed in 1994, that in the same class of experiments Jeffreys' prior is asymptotically optimal in the sense of Shannon, or, in Bayesian terms, Jeffreys' prior is asymptotically least favorable under Kullback Leibler risk. In the present paper, we prove, based on Clarke and Barron's results, that every sequence of Shannon optimal priors on a sequence of regular iid product experiments converges weakly to Jeffreys' prior. This means that for increasing sample size Kullback Leibler least favorable priors tend to Jeffreys' prior.