Optimum group designs for random-effects nonlinear dynamic processes

We give the theoretical background and an algorithm for calculating optimum group experimental designs for regression models with random model parameters. The theory is applicable to those practical situations in which a dynamical system is sensitive to sampling or gives a different response at each run of the experiment. This difference in response is due both to the inherent nature of the system and to random noise in the observations. We treat all observations as independent. Together with the definition of the group designs that we introduce, this structure leads to a practical and numerically tractable representation of optimum designs for estimation of the mean values of the parameters. We present two different examples of chemical reactions where such modelling of the random structure is particularly relevant, one for a single response, the other for multivariate data.