SEQUENTIAL INFORMATION SEEKING: AN OPTIMAL STRATEGY AND OTHER RESULTS
NORTH CAROLINA UNIV AT CHAPEL HILL PSYCHOMETRIC LAB
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This paper presents an optimal strategy for sequential sampling from binomial distributions. The strategy presented is general in that it is a multi-action rather than a two-action procedure. While the major task is to estimate the proportion, p, of successes in a hypothetical, infinite population of binary observations, it is assumed that the decision maker is only concerned with which of a set of mutually exclusive and exhaustive subsets of the unit interval contains p. The derived strategy maximizes the decision- makers gain without regard to error probabilities. The important variable in determining a rule for ceasing to look at new data and making a decision is found to be the expected probability of being correct. The criterion involves only the economic aspects of the situation. A no information theorem is presented which shows that under some circumstances when a success or a failure on a given trial are equally probable, the probability of being correct after making the observation is identical to the probability of being correct before the observation was taken. Finally, an appealing derivation of the Beta-binomial probability function is given which suggests a more tractable computational procedure for the distribution and which illuminates its limiting distribution.
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