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EMPIRICAL BAYES DETECTION OF A CHANGE

IN DISTRIBUTION

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ROHANA J. KARUNAMUNI AND SHUNPU ZHANG

*Department of Mathematical Sciences, University of Alberta,*

Edmonton, Alberta, Canada T6G 2G1
(Received August 22, 1994; revised March 31, 1995)

**Abstract.**
The problem of detection of a change in
distribution is considered. Shiryayev (1963, *Theory Probab.
Appl.*, **8**, pp.22-46, 247-264 and 402-413; 1978,
*Optimal Stopping Rules*, Springer, New York) solved the problem in
a Bayesian framework assuming that the prior on the change point is
Geometric (*p*). Shiryayev showed that the Bayes solution prescribes
stopping as soon as the posterior probability of the change having
occurred exceeds a fixed level. In this paper, a myopic policy is
studied. An empirical Bayes stopping time is investigated for
detecting a change in distribution when the prior is not completely
known.

*Key words and phrases*:
Empirical Bayes, change points,
Bayes sequential rules, stopping times, statistical process control.

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