Behrens–Fisher problem Is there a good published expository account, with mathematical details, of the various approaches that have been taken to the Behrens–Fisher problem?
 A: This article by L. J. Savage in 1976 was the motivation for a seminar we held for graduate students and professors at Stanford in 1977.  I was  a student then and gave my talk on the Behrens-Fisher problem.  Faculty and visiting faculty participating included Seymour Geisser, Brad Efron and David Hinkley (and possibly other that I can't recollect). Paper from Annals of Statistics 1976 "On Rereading R. A. Fisher."  The work and controversy on the Behren's-Fisher problem was one of many topics discussed through Savage's interpretation of Fisher's writings which I think included some heated debates. One with M. S. Barlett in particular.  Savage points to the gems of wisdom more than this one flaw.  This problem was the one that exposed the difference between fiducial inference and the Neyman-Pearson hypothesis testing approach. Prior to that Fisher recognized philosophical differences but thought that the two methods gave the same answers.  But they do differ when nuisance parameters are involved (in the case of Behrens-Fisher the unknown population variance).
Link
In the questioning period of my talk I discovered that Seymour Geisser was like an encyclopedia on this problem.  you may find his book (published around the time of his death) Modes of Statistical Inference which is a rare book that discusses fiducial inference along with frequentist and Bayesian approaches. here is an amazon link for that.
This link also contains my customer review of the book which includes a lot of what I have said here about Seymour. Modes of Parametric Statistical Inference by Seymour Geisser and Wesley Johnson.
Modes of Parametric Statistical Inference 1st Edition
A: Chuanhai Liu recently developed an interesting framework of statistical inference, called 'Inferential Model'. Behrens-Fisher problem is one of the examples which can be quite elegantly tackled using this framework; if interested, take a look at Chapter 4.2 of the following paper: "Marginal inferential models: prior-free probabilistic
inference on interest parameters" by Ryan Martin
http://www.stat.purdue.edu/~chuanhai/docs/immarg.pdf
It also contains some references to a number of key papers and review papers. I am not an expert on this topic, so I am not sure how comprehensive the reference is, but I guess it could be a good starting point!
