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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 978691, 5 pages
Research Article

Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence

School of Economics, Beijing Technology and Business University, Beijing 100048, China

Received 13 October 2013; Accepted 28 January 2014; Published 4 March 2014

Academic Editor: Francis T. K. Au

Copyright © 2014 Yuliang Yin and Baoren Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Behrens-Fisher problem concerns the inferences for the difference between the means of two normal populations without making any assumption about the variances. Although the problem has been extensively studied in the literature, researchers cannot agree on its solution at present. In this paper, we propose a new method for dealing with the Behrens-Fisher problem in the Bayesian framework. The Bayesian evidence for testing the equality of two normal means and a credible interval at a specified level for the difference between the means are derived. Simulation studies are carried out to evaluate the performance of the provided Bayesian evidence.