Robust static designs for approximately specified nonlinear regression models

We outline the construction of robust, static designs for nonlinear regression models. The designs are robust in that they afford protection from increases in the mean squared error resulting from misspecifications of the model fitted by the experimenter. This robustness is obtained through a combination of minimax and Bayesian procedures. We first maximize (over a neighborhood of the fitted response function) and then average (with respect to a prior on the parameters) the sum (over the design space) of the mean squared errors of the predictions. This average maximum loss is then minimized over the class of designs. Averaging with respect to a prior means that there is no remaining dependence on unknown parameters, thus allowing for static, rather than sequential, design construction. The minimization over the class of designs is carried out by implementing a genetic algorithm. Several examples are discussed.