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Biometrika 1967 54(1-2):326-328; doi:10.1093/biomet/54.1-2.326
© 1967 by Biometrika Trust
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MISCELLANEA

The empirical Bayes approach: estimating the prior distribution

J. R. RUTHERFORD * and R. G. KRUTCHKOFF

Virginia Polytechnic Institute

There is a random variable A distributed according to a specific but unknown prior distribution G from an appropriate class GP. The random variable {Lambda} = {lambda} is unobrvable but another random variable X = x, distributed with known conditional distribution function F(x|{lambda}), is observable. We construct estimators Gn({lambda}) of G({lambda}) such that lim E[{Gn({lambda}) – G({lambda})}2]=0 and we use Gn({lambda}) to estimate the posterior distribution G({lambda}|x) and hence to construct consistent estimators of posterior confidence intervals.


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