Bayesian Analysis

Comparing normal means: new methods for an old problem

José M. Bernardo and Sergio Pérez

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Comparing the means of two normal populations is an old problem in mathematical statistics, but there is still no consensus about its most appropriate solution. In this paper we treat the problem of comparing two normal means as a Bayesian decision problem with only two alternatives: either to accept the hypothesis that the two means are equal, or to conclude that the observed data are, under the assumed model, incompatible with that hypothesis. The combined use of an information-theory based loss function, the intrinsic discrepancy (Bernardo and Rueda 2002}, and an objective prior function, the reference prior \citep{Bernardo 1979; Berger and Bernardo 1992), produces a new solution to this old problem which has the invariance properties one should presumably require.

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Bayesian Anal., Volume 2, Number 1 (2007), 45-58.

First available in Project Euclid: 22 June 2012

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Bayes factor BRC comparison of normal means intrinsic discrepancy precise hypothesis testing reference prior two sided tests


Bernardo, José M.; Pérez, Sergio. Comparing normal means: new methods for an old problem. Bayesian Anal. 2 (2007), no. 1, 45--58. doi:10.1214/07-BA202.

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