A Bayesian solution to the Behrens–Fisher problem
Fco. Javier Girón, Carmen Castillo-Vázquez · Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas · 2021
Abstract A simple solution to the Behrens–Fisher problem based on Bayes factors is presented, and its relation with the Behrens–Fisher distribution is explored. The construction of the Bayes factor is based on a simple hierarchical model, and has a closed form based on the densities of general Behrens–Fisher distributions. Simple asymptotic approximations of the Bayes factor, which are functions of the Kullback–Leibler divergence between normal distributions, are given, and it is also proved to be consistent. Some examples and comparisons are also presented.