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Our main intent is to introduce the reader to the statistical area that in rather loose terms can be called “model-based optimal design of experiments.” The word “design” implies that there exist some variables, the values of which can be chosen in the planning stage. We focus our exposition on cases when a researcher can describe the relation between these variables and responses (response variables) by means of a mathematical model that describes the observed system. Often the system description is based on the deterministic model while the observational component is modeled via stochastic mechanisms. However, it is not always the case: biological systems or clinical trials are good examples of when stochastic models can be used for system description as well. See, for instance, examples in Section 7.4 where stochastic differential equations are used to model intrinsic patient variability in pharmacokinetic studies. Regression models with random parameters provide another example of such a setting.
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