OPTIMIZING NONADAPTIVE GROUP TESTS FOR OBJECTS WITH HETEROGENEOUS PRIORS

We investigate nonadaptive group testing designs for heterogeneous mix tures of objects, independently positive with individual prior probabi lities. In our model of the prior probabilities, the objects occur in one of several disjoint subsets and the number of positives in each su bset is known. Furthermore, the positives are ''uniformly distributed' ' within the subsets. The expected number of unresolved negative objec ts is minimized, and a unique global minimum is found for a family of stochastic, random incidence designs: all v group tests are constructe d independently. The optimum incidence probabilities for the objects a re well approximated by an asymptotic power series in v(-1). We find t he three leading coefficients of this series. The dependence of the op timum incidence probability upon the prior probability is, to leading order, logarithmic. Objects with larger prior probability of being pos itive have smaller optimum incidence probability. Furthermore, this lo garithmic dependence can be nonnegligible for screening collections of cloned DNA sequences.