Two Modeling Strategies for Empirical Bayes Estimation

Empirical Bayes methods use the data from parallel experiments, for instance, observations Xₖ(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.