A monte carlo study of the performance of a closed adaptive sequential procedure for selecting the best bernoulli population

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Abstract
The performance characteristics of a closed adaptive sequential procedure for selecting the best Bernoulli population, recently proposed by Bechhofer and Kulkarni, are studied using Monte Carlo simulation. The sequential procedure has been shown to achieve the same probability of a correct selection, uniformly in the unknown single-trial "success" probabilities p i (1≦i≦k) as does the corresponding single-stage procedure which takes exactly n observations from each of the k populations; in addition, has been shown to possess severa! highly desirable optimal properties. In the present paper we obtain precise MC estimates of E{N(i)} (1≦i≦k) and E{N) where N (i) is the total number of observations taker. from the population associated with p (i) (1≦i≦k) when terminates sampling, and here are the ordered p i (1≦i≦k) MC estimates of other related performance characteristics are also obtained. Special emphasis is given to k = 4 and 5 populations for which no results had been obtained heretofore because of the costs associated with calculating exact results. It is shown in that very substantia! savings in E{N} can be realized if is used in place of the corresponding single-stage procdure. It is also shown that samples much less frequently from the populations having the smaller p-values, thus making it particular!y attractive for use in clinical trials. For each k and n, the results are given for many , and hence an experimenter with some prior notion as to the approximate range within which his true p [i](1≦i≦k) lie, can assess the potential gains that can be achieved by using

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