EMPIRICAL BAYES DETECTION OF A CHANGE IN DISTRIBUTION

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.