Sets pooling designs (Q1306748)

A pooling design is a collection of subsets, called pools, of a finite set \(U\). Conventional pooling designs are used to identify distinguished (positive) elements of \(U\). Provided there are no experimental errors, a pool containing at least one positive object yields a positive assay. The author introduces the notion of positive subset, so that a pool yields a positive assay when it contains a positive subset. Sets pooling designs generalise conventional pooling designs and their introduction is motivated by modern molecular and cellular biology. The feasibility of constructing sets pooling designs is discussed by investigating random, non-adaptive designs in the case all distinguished subsets have the same size. Deterministic and adaptive designs are described, too. An interesting formula is proved for an optimum probability for including an object in a pool.