Screening by Conference Designs

Screening experiments are addressed to the identiication of the relevant variables within some process or experimental outcome potentially depending on a large number of variables. In this paper we introduce a new class of experimental designs called edge designs. These designs are very useful for screening experiments since they allow a model-independent estimate of the set of relevant variables, thus providing more robustness than traditional designs. We give a bound on the determinant of the information matrix of certain edge designs, and show that a large class of edge designs meeting this bound can be constructed from conference matrices. We also show that the resulting conference designs have an optimal space exploration property which is important as a guard against unexpected nonlinearities. We survey the existence of and constructions for conference matrices, and give, for n < 50 variables, explicit such matrices when n is a prime, and references to explicit constructions otherwise.