Structure of Optimal Samples in Continuous Nonlinear Experimental Design for Parameter Estimation
In the continuous case, Optimal Experimental Design (OED) deals with designs that are described by probability distributions or samples over the experimental domain. An optimal design may correspond to a distribution having finite or infinite support or being continuous. In this paper, the structure of optimal samples for experimental designs is elucidated. It is shown that any design is in fact equivalent to a design with a finite number of support points. The lower bound and upper bound of this number, especially for optimal designs, are given and examples indicate their sharpness. Moreover, we propose an algorithm to construct optimal designs which have finite support. Several applications to OED for dynamic systems with inputs are also discussed.
The authors would like to thank anonymous reviewers for their constructive comments. The first author’s research is funded by the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences.
- 2.Bock, H.G., Körkel, S., Schlöder, J. P.: Parameter estimation and optimal experimental design for nonlinear differential equation models. In Bock, H.G., Carraro, T., Jäger, W., Körkel, S., Rannacher, R., Schlöder, J.P. (eds.) Model Based Parameter Estimation: Theory and Application, vol. 4, pp. 1–30. Springer, Berlin (2013)CrossRefGoogle Scholar
- 4.Körkel, S.: Numerische Methoden für Optimale Versuchsplanungsprobleme bei nichtlinearen DAE-Modellen. PhD thesis, Universität Heidelberg (2002)Google Scholar