Group testing with a new goal, estimation

Abstract

The ideas of group testing, i.e. of testing units in batches instead of individually, where each test only indicates whether the tested baton contains only good units or whether it contains at least one defective, is applied to the problem of estimating the probability p of an arbitrary unit being defective. A certain class of nested halving procedures is shown to be highly efficient and the saving over the one-at-a-time procedures is even greater for the estimation problem than for the previously treated group-testing problems of classifying all the units in a given finite set. The main criterion used for evaluating efficiency in this paper is the asymptotic cost per unit information when a large number of tests are carried out. This paper deals only with the large-sample aspects of the problem. Tables are given that explicitly describe how to carry out the procedure and other tables indicate how close the results are to those of optimal procedures for certain input parameters.