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The problem of finding a single defective item from an infinite binomial population is considered when group-testing is possible, i.e., when we can test any number of units x simultaneously and find out in one test if oil x are good or if at least one of the x is defective. An optimal procedure is obtained in the sense that it minimizes the expected number of tests required to find one defective. Upper and lower bounds are derived using information theory and the relation of our procedure to the Huffman algorithm and the corresponding cost is studied. [ABSTRACT FROM AUTHOR]

n an information-processing chain, only the initial inputs ("environment") and the terminal outputs ("actions") affect directly the benefit to the user who maximizes its expected excess over cost. All intermediate flows ("symbols") affect directly only costs and delays. Delays affect benefit non-additively, through "impatience"and, possibly, "obsolescence." Traditionally, statistical theory disregards delays,and communication theory treats them as costs. A more complete, unifying approach is proposed, and it is asked whether convexity conditions (e.g., "decreasing marginal returns") required for competitive market equilibrium are satisfied. [ABSTRACT FROM AUTHOR]

A lower bound is derived concerning a special form of the entropy function of information theory. It is applied to Hoeffding's bound for the probability of the deviation of the sample mean from its expected value and for the corresponding problem concerning the sample variance. Furthermore, applying the bound one can obtain a discard function for a binary symmetric channel, a lower bound for the total error probability in testing two simple hypotheses, given the number of observations, and a lower bound for the deviation of the empirical distribution from the true distribution. [ABSTRACT FROM AUTHOR]