Experimental Design for Nonlinear Problems

Abstract

Experimental designs for nonlinear problems have to a large extent relied on optimality criteria originally proposed for linear models. Optimal designs obtained for nonlinear models are functions of the unknown model parameters. They cannot, therefore, be directly implemented without some knowledge of the very parameters whose estimation is sought. The natural way is to adopt a sequential or Bayesian approach. Another is to utilize available estimates or guesses. In this article we provide a brief historical account of the subject, discuss optimality criteria commonly used for nonlinear models, the associated problems and ways of overcoming them. We also discuss issues of robustness of locally optimal designs. A brief review of sequential and Bayesian procedures is given. Finally we discuss alternative design criteria of constant information and minimum bias and pose some problems for future work.