Optimal discriminating designs for several competing regression models

TL;DR

This paper develops an efficient algorithm for constructing optimal discriminating designs among multiple regression models, overcoming computational challenges and outperforming existing methods in complex comparison scenarios.

Contribution

The authors introduce a novel algorithm based on vector-valued approximation for optimal discriminating design construction, improving over existing methods especially with many pairwise model comparisons.

Findings

The new algorithm successfully finds optimal designs where previous methods fail.

Numerical examples demonstrate improved efficiency and accuracy of the proposed approach.

The method effectively handles complex model comparison scenarios with multiple pairwise comparisons.

Abstract

The problem of constructing optimal discriminating designs for a class of regression models is considered. We investigate a version of the $T_p$-optimality criterion as introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 289-303]. The numerical construction of optimal designs is very hard and challenging, if the number of pairwise comparisons is larger than 2. It is demonstrated that optimal designs with respect to this type of criteria can be obtained by solving (nonlinear) vector-valued approximation problems. We use a characterization of the best approximations to develop an efficient algorithm for the determination of the optimal discriminating designs. The new procedure is compared with the currently available methods in several numerical examples, and we demonstrate that the new method can find optimal discriminating designs in situations where the currently available procedures fail.