Optimal experimental design: from design point to design region

Optimal experimental designs are used in chemical engineering to obtain precise mathematical models. The optimal design consists of design points with a maximal amount of information and thus lead to more precise models than statistical designs. In general, the optimal design depends on an uncertain estimate of unknown model parameters. The optimal designs are therefore also uncertain and continuously shift in the design space, as the value of changes. We present two approaches to capture this behavior when computing optimal designs, a global clustering approach and a local approximation of the confidence regions. Both methods find an optimal design and assign the optimal design points confidence regions which can be used by an experimenter to decide which design points to use. The clustering approach requires a Monte Carlo sampling of the uncertain parameters and then identifies regions of high weight density in the design space. The local approximation of the confidence regions is obtained via an error propagation using the derivatives of the optimal design points and weights. We apply the introduced approaches to mathematical examples as well as to an application example modeling vapor-liquid equilibria.