Computation Aspects on the Nonlinear Designs

• Activity Number: 190
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Christos Kitsos*+
• Companies: Technological Educational Institute of Athens
• Keywords: Beale's measure ; confidence region ; calibration ; curvature

Abstract

When fitted a nonlinear model, this is selected among various nonlinear models. One of the targets of this paper is to discuss the computation criteria , applied for the selection of the appropriate nonlinear models and the optimal design linked with the proposed model. An optimal design is the one that eventually concludes to the optimal estimation of the parameters. Various optimality criteria exist, the most well-known being the D-optimality: the one that minimizes the variances of all the included parameters of the assumed nonlinear model under investigation. Computationally the nonlinear problem is approached by a first order Taylor approximation, as a second order Taylor approximation might create more problems than those which try to solve. The nonlinearity influences the confidence regions and therefore Beale's measure of nonlinearity is adopted. The second target of this paper is to provide an easy approximation of this measure, useful for the experimenter. The method is applied to the calibration problem, which is faced as an optimal experimental design.