Pareto-optimal designs - computer simulation experiments for alternatives to G-optimal designs
Sprache des Vortragstitels:
Sprache des Tagungstitel:
A popular criterion for minimizing the variance of estimates in experimental design is G-optimality. A G-optimal design is a design that minimizes the maximal variance of the predicted values. If we use kriging methods for prediction it is self-evident to use the kriging variance as a measure of uncertainty for the estimates. Though the computation of the corrected kriging variance is a very costly task and finding the maximal kriging variance in high-dimensional regions can be computationally and time demanding such that we cannot really find the G-optimal design with nowadays available computer equipment in practice.
D-optimality is another design criterion. A D-optimal design maximizes the determinant of the information matrix of the estimates. D-optimality in terms of trend parameter estimation and D-optimality in terms of covariance parameter estimation yield basically different designs. The Pareto frontier of these two determinant criteria corresponds with designs that perform well under both criteria.
Under certain conditions searching the G-optimal design on the above Pareto frontier yields almost as good results as searching the G-optimal design in the whole design region. In doing so the maximal kriging variance has to be computed only a few times though.
The method is demonstrated by means of a computer simulation experiment based on data provided by the Belgian institute Management Unit of the North Sea Mathematical Models (MUMM).