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Bayes procedures for deciding the Sign of a normal mean

Published online by Cambridge University Press:  24 October 2008

J. A. Bather  and
A. M. Walker
J. A. Bather
Affiliation:
Statistical Laboratory Cambridge
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Abstract

The decision problem discussed concerns the drift of a Wiener process with known variance per unit time. It is required to find the optimal sequential test for the sign of the drift, when sampling costs and the cost of a wrong terminal decision are specified. Initially, the drift is supposed to have a continuous prior distribution. The optimal procedure is determined by a continuation region in which a certain partial differential equation holds. The boundaries of this region can be found explicitly in a few special cases. In general, methods are developed for obtaining both inner and outer approximations to the optimal continuation region and these techniques are illustrated by application to several examples.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 4 , October 1962 , pp. 599 - 620
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

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