### Abstract

A hierarchical Bayesian approach to the problem of comparison of two means is considered. Hypothesis testing, ranking and selection, and estimation (after selection) are treated. Under the hypothesis that two means are different, it is desired to select the population which has the larger mean. Expressions for the ranking probability of each mean being the larger and the corresponding estimate of each mean are given. For certain priors, it is possible to express the quantities of interest in closed form. A simulation study has been done to compare mean square errors of a hierarchical Bayesian estimator and some of the existing estimators of the selected mean. The case of comparing two means in the presence of block effects has also been considered and an example is presented to illustrate the methodology.

Original language | English (US) |
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Pages (from-to) | 3785-3800 |

Number of pages | 16 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 18 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 1989 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Cite this

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*Communications in Statistics - Theory and Methods*, vol. 18, no. 10, pp. 3785-3800. https://doi.org/10.1080/03610928908830123

**A Bayesian Approach to the Comparison of Two Means.** / Fong, Duncan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A Bayesian Approach to the Comparison of Two Means

AU - Fong, Duncan

PY - 1989/1/1

Y1 - 1989/1/1

N2 - A hierarchical Bayesian approach to the problem of comparison of two means is considered. Hypothesis testing, ranking and selection, and estimation (after selection) are treated. Under the hypothesis that two means are different, it is desired to select the population which has the larger mean. Expressions for the ranking probability of each mean being the larger and the corresponding estimate of each mean are given. For certain priors, it is possible to express the quantities of interest in closed form. A simulation study has been done to compare mean square errors of a hierarchical Bayesian estimator and some of the existing estimators of the selected mean. The case of comparing two means in the presence of block effects has also been considered and an example is presented to illustrate the methodology.

AB - A hierarchical Bayesian approach to the problem of comparison of two means is considered. Hypothesis testing, ranking and selection, and estimation (after selection) are treated. Under the hypothesis that two means are different, it is desired to select the population which has the larger mean. Expressions for the ranking probability of each mean being the larger and the corresponding estimate of each mean are given. For certain priors, it is possible to express the quantities of interest in closed form. A simulation study has been done to compare mean square errors of a hierarchical Bayesian estimator and some of the existing estimators of the selected mean. The case of comparing two means in the presence of block effects has also been considered and an example is presented to illustrate the methodology.

UR - http://www.scopus.com/inward/record.url?scp=0011584602&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011584602&partnerID=8YFLogxK

U2 - 10.1080/03610928908830123

DO - 10.1080/03610928908830123

M3 - Article

AN - SCOPUS:0011584602

VL - 18

SP - 3785

EP - 3800

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 10

ER -