Optimal fractional factorial split-plot designs for model selection

Fractional factorial designs are used widely in screening experiments, where significant effects are identified. It is not always possible to perform the trials in a complete random order and hence, fractional factorial split-plot designs arise. In order to identify optimal fractional factorial split-plot designs in this setting, the Hellinger distance criterion (Bingham and Chipman (2007)) is proposed. The approach is Bayesian and directly incorporates common experimenter assumptions. By specifying prior distributions for the model space, the criterion for fractional factorial split-plot designs aims to discriminate between the most probable competing models. Techniques for evaluating the criterion and searching for optimal designs are proposed. The criterion is then illustrated through a few examples with further discussion on the choice of hyperparameters and flexibility of the criterion.