Abstract
Empirical Bayes methods use the data from parallel experiments, for instance observations X(k) ~ 𝒩 (Θ (k) , 1) for k = 1, 2, …, N, to estimate the conditional distributions Θ (k) |X(k) . There are two main estimation strategies: modeling on the θ space, called "g-modeling" here, and modeling on the×space, called "f-modeling." The two approaches are de- scribed 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.