A0262
Title: Optimal designs under model uncertainty
Authors: Xietao Zhou - KCL (United Kingdom) [presenting]
Steven Gilmour - KCL (United Kingdom)
Abstract: Traditional optimal designs are optimal under the pre-specified model. When the final fitted model differs from the pre-specified model, traditional optimal designs may cease to be optimal, and the corresponding parameter estimators may have larger variances. The $Q_B$ criterion has been proposed to consider hundreds of alternative models that could appear for multifactor designs in the sense that the $Q_B$-optimal design shall give better parameter estimation in more alternative models than the traditional optimal designs. Recently, an alternative parameterization of factorial designs called baseline parameterization has been considered in the literature. It has been argued that such a parameterization arises naturally if there is a null state of each factor, and the corresponding optimal design has been explored. The basic framework of the $Q_B$ criterion and how it could be extended to the baseline parameterization is introduced. Some $Q_B$-optimal designs found are then presented, and it is shown that they have achieved advantages in terms of traditional $A_S$-optimality versus the optimal designs in previous literature for various specified prior probabilities of main effects and two-factor interactions being in the best model.
