title: Two modeling strategies for empirical Bayes estimation.
abstract: Empirical Bayes methods use the data from parallel experiments, for instance observationsXk~ 𝒩 (Θk, 1) fork= 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×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.
authors.affiliation: Stanford University.
authors.forename: Bradley
authors.initials: B
authors.lastname: Efron
keywords: Bayes rule in terms of f; f-modeling; g-modeling; prior exponential families