Two modeling strategies for empirical bayes estimation

Abstract

Empirical Bayes methods use the data from parallel experiments, for instance, observations Xk ~ N(Θk, 1) for k = 1, 2,..., N, to estimate the conditional distributions Θk|Xk. There are two main estimation strategies: modeling on the Θ 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.