Statistical Science

Two Modeling Strategies for Empirical Bayes Estimation

Bradley Efron

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Empirical Bayes methods use the data from parallel experiments, for instance, observations $X_{k}\sim\mathcal{N}(\Theta_{k},1)$ for $k=1,2,\ldots,N$, to estimate the conditional distributions $\Theta_{k}|X_{k}$. There are two main estimation strategies: modeling on the $\theta$ space, called “$g$-modeling” here, and modeling on the $x$ space, called “$f$-modeling.” The two approaches are described and compared. A series of computational formulas are developed to assess their frequentist accuracy. Several examples, both contrived and genuine, show the strengths and limitations of the two strategies.

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Statist. Sci., Volume 29, Number 2 (2014), 285-301.

First available in Project Euclid: 18 August 2014

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$f$-modeling $g$-modeling Bayes rule in terms of $f$ prior exponential families


Efron, Bradley. Two Modeling Strategies for Empirical Bayes Estimation. Statist. Sci. 29 (2014), no. 2, 285--301. doi:10.1214/13-STS455.

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