An empirical bayes approach to the Behrens‐Fisher problem

摘要

AbstractThis paper is inspired by recent work of G.A. Barnard, who treats the Behrens‐Fisher problem from a Bayesian point of view, and provides calculator programs to implement the solutions (including the classical fiducial solution). We review Barnard's work, and generalize his family of priors in a manner that makes it convenient to estimate the form of the prior from the observed variance ratio. A calculator program is provided to give an empirical estimate (based on marginal maximum likelihood), in an interesting special case, of a parameter of the prior distribution. In addition, programs similar to Barnard's are provided to calculate Bayes or Empirical Bayes p‐values and confidence interv