Two modeling strategies for empirical Bayes estimation

Stat Sci. 2014 May;29(2):285-301. doi: 10.1214/13-sts455.

Abstract

Empirical Bayes methods use the data from parallel experiments, for instance observations Xk ~ 𝒩 (Θ k , 1) for k = 1, 2, …, N, to estimate the conditional distributions Θ k |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.

Keywords: Bayes rule in terms of f; f-modeling; g-modeling; prior exponential families.