Simulation-based optimal experimental design techniques provide a set of tools to solve model-based experimental design problems for complex models. The goal of optimal experimental design is to determine the factor settings prior to conducting the experiment so as to minimize the sampling effort. Further complications arise if the likelihood function is intractable, which is the case in many modern statistical models for areas such as biogenetics, epidemiology, or extremes.
In this thesis, several strategies are proposed to adapt simulation-based optimal design techniques to cope with intractable likelihoods. This is accomplished by incorporating ideas from approximate Bayesian computation (ABC) methods, also called likelihood-free methods. On the one hand, the simulation-based design methods initiated by Peter Müller are extended to deal with intractable likelihoods when prior observations are available. In a second line of work, ABC methods are generally used to approximate Bayesian design criteria, which are based on the posterior distribution. The design criteria have to be re-evaluated many times during a simulation-based optimal design algorithm, which poses challenges that can be resolved by employing and designing appropriate ABC methods.
The methods are applied to several examples. The most prominent application is the search for the optimal network of weather stations for a spatial extremes setting modeled by max-stable processes.