Statistical Science

Two Modeling Strategies for Empirical Bayes Estimation

Bradley Efron

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 18 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.ss/1408368582

Digital Object Identifier
doi:10.1214/13-STS455

Mathematical Reviews number (MathSciNet)
MR3264543

Zentralblatt MATH identifier
1332.62031

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

Citation

Efron, Bradley. Two Modeling Strategies for Empirical Bayes Estimation. Statist. Sci. 29 (2014), no. 2, 285--301. doi:10.1214/13-STS455. https://projecteuclid.org/euclid.ss/1408368582


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