The empirical Bayes approach: estimating the prior distribution

Abstract

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