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An empirical bayes approach to the Behrens‐Fisher problem
Author(s) -
Duong Q. P.,
Shorrock R. W.
Publication year - 1992
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.3170030204
Subject(s) - bayes' theorem , calculator , prior probability , point estimation , marginal likelihood , bayes factor , bayesian probability , computer science , statistics , econometrics , mathematics , variance (accounting) , economics , accounting , operating system
This 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 intervals.