Sequential Information Seeking: an Optimal Strategy and Other Results. Esd-tdr-64-605.

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 twoaction 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-maker's 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 Betabinomial probability function is given which suggests a more tractable computational procedure for the distribution and which illuminates its limiting distribution.