## Bayesian Analysis

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

### Comparing normal means: new methods for an old problem

José M. Bernardo and Sergio Pérez

#### Abstract

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.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 22 June 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.ba/1340390062

**Digital Object Identifier**

doi:10.1214/07-BA202

**Mathematical Reviews number (MathSciNet)**

MR2289922

**Zentralblatt MATH identifier**

1331.62121

**Subjects**

Primary: Database Expansion Item

**Keywords**

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

#### Citation

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. https://projecteuclid.org/euclid.ba/1340390062