Design of experiments for discrimination of rival models based on the expected number of eliminated models

Abstract

This work presents a new design criterion for discrimination of rival models, taking into account the number of models that are expected to be discriminated after execution of the experimental design (ξ⁎). The potential for model discrimination at ξ⁎ can be calculated by assuming that model m is the true one. In this case, responses can be predicted with model m at ξ⁎, parameters of the remaining models can be re-estimated and model adequacy tests can be performed in order to compute the number of discriminated models. Since several rival models are considered simultaneously and the true model is not known a priori, the potential for model discrimination at ξ⁎ should be evaluated for pair-wise comparisons of the plausible models. As a consequence, Maxmin, Bayesian or Equal Model Weights optimization criteria must be adopted to select the best experimental conditions in the Pareto set for discrimination of rival models within the scope of a sequential design procedure. The proposed approach leads to formulation of an informative design criterion, where the discriminant value can be easily interpreted in terms of the expected number of eliminated models.