Two Modeling Strategies for Empirical Bayes Estimation

Abstract

Empirical Bayes methods use the data from parallel experiments, for instance, observations $X_k\sim \mathcal{N}({\Theta }_k,1)$ for $k=1,2,\dots ,N$, 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.

Published in at http://dx.doi.org/10.1214/13-STS455 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• A ridge-parameter approach to deconvolution
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• Detecting mutations in mixed sample sequencing data using empirical Bayes