Multiplicative methods for computing D-optimal stratified designs of experiments

Consider a linear regression experiment with uncorrelated real-valued observations and a finite design space. An approximate experimental design is stratified if it allocates given proportions of trials to selected non-overlapping partitions of the design space. To calculate an approximate D-optimal stratified design, we propose two multiplicative methods: a re-normalisation heuristic and a barycentric algorithm, both of which are very simple to implement. The re-normalisation heuristic is generally more rapid, but for the barycentric algorithm, we can prove monotonic convergence to the optimum. We also develop rules for the removal of design points that cannot support any D-optimal stratified design, which significantly improves the speed of both proposed multiplicative methods.