ABSTRACT
The topic of this part of the handbook-optimal design for nonlinear and spatial modelsallows for a very broad range of subtopics. We should first distinguish these from those formulated for linear models. A salient feature of design problems for linear models is that the common functions expressing the experimenter’s loss, when estimating the mean response, do not depend on the unknown parameters being estimated. In this chapter, a number of design problems are introduced in which this very convenient feature is absent, and ways of dealing with its absence are discussed in general terms. Thus, although we treat classical nonlinear regression models in which a response variable y is measured with additive error and E [y|x] is a nonlinear function of parameters θ to be estimated after the experiment is conducted, there is a multitude of other applications. In this chapter, these subjects will be introduced in broad generality only, and some historical context provided; precise details and examples are given in the three chapters which follow:
• Designs for Generalized Linear Models (Chapter 13) • Designs for Selected Nonlinear Models (Chapter 14) • Optimal Design for Spatial Models (Chapter 15) Chapters 22, 24 and 25 deal with special applications that use nonlinear models.
