Generalized BayesianDcriterion for single‐stratum and multistratum designs

Abstract

AbstractThe BayesianDcriterion modifies theD‐optimality approach to reduce dependence of the selected design on an assumed model. This criterion has been applied to select various single‐stratum designs for completely randomized experiments when the number of effects is greater than the sample size. In many industrial experiments, complete randomization is sometimes expensive or infeasible, and hence, designs used for the experiments often have multistratum structures. However, the original BayesianDcriterion was developed under the framework of single‐stratum structures and cannot be applied to select multistratum designs. In this paper, we study how to extend the Bayesian approach for more complicated experiments and develop the generalized BayesianDcriterion, which generalizes the original BayesianDcriterion and can be applied to select single‐stratum and multistratum designs for various experiments when the number of effects is greater than the rank of the model matrix.