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The Scientific World Journal
Volume 2013 (2013), Article ID 381539, 7 pages
Research Article

Testing Normal Means: The Reconcilability of the Value and the Bayesian Evidence

1School of Economics, Beijing Technology and Business University, Beijing 100048, China
2School of Mathematics and System Science, Beihang University, LMIB of the Ministry of Education, Beijing 100083, China

Received 8 August 2013; Accepted 9 September 2013

Academic Editors: M. Guillén and S. Umarov

Copyright © 2013 Yuliang Yin and Junlong Zhao. 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 problem of reconciling the frequentist and Bayesian evidence in testing statistical hypotheses has been extensively studied in the literature. Most of the existing work considers cases without the nuisance parameters which is not the frequently encountered situation since the presence of the nuisance parameters is very common in practice. In this paper, we consider the reconcilability of the Bayesian evidence against the null hypothesis in terms of the posterior probability of being true and the frequentist evidence against in terms of the value in testing normal means where the nuisance parameters are present. The reconcilability of evidence can be obtained both for testing a normal mean and for the Behrens-Fisher problem.