Criteria for Factorial Designs Under Model Uncertainty

Abstract

This talk is concerned with designing multifactor experiments when experimenters do not in advance know what model will be fitted. In the case of design under model uncertainty, different criteria are used in different situations. In this talk, we provide a unified framework for selecting a design in different types of designs under different experimental objectives. A general criterion, called QB, for design under model uncertainty is introduced and applications of this criterion to different design problems are presented. Some notation for the generalised word count which represents an overall measure of the partial aliasing and correlations of the factorial effects is also defined. We use the generalised word count to summarise relationships between QB and the various generalised aberration and other criteria used for different design problems. It is shown that the E(s2) criterion for supersaturated designs is a special case of QB and several aberration and generalized aberration criteria are closely related to QB. We show that the QB criterion, which aims to improve the estimation in as many models as possible, is more general and has a better statistical justification than the standard criteria and can be recommended for many practical experiments.