The Statistical Design and Analysis of Experiments for Large-scale Computer Simulators

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Recent gains in computational power have increased our ability to simulate complex physical phenomena. With these gains comes the potential to investigate scientific questions that historically would have been addressed only through expensive physical experimentation, if at all. Examples of exploration of complex systems via computational models is common in science, with recent applications ranging from astrophysics to climate change to the study micro-scale organisms, etc., the list goes on and on. In fact, the recent Intergovernmental Panel on Climate Change (IPCC) report contains several conclusions that are based on inference to the real world using computational models. In some applications, simulation of the system is computationally expensive making the choice of inputs (the experimental design) to the model a critical task of the study. In other settings, interest lies in combining simulations and field data. Still, in other situations, the simulator may be fast, but the number of model runs can be high. In any case, there are many pressing problems of interest to scientists and industrial researchers that need to be addressed to effectively utilize their computer models. The proposed research will develop new statistical methodology for computer experiments. Specific projects include (i) modeling output from deterministic computer simulators; (ii) combining field data and computer model outputs for discrete data to make inferences about physical processes; and (iii) modeling large ensembles of simulator runs. New experimental designs will be proposed that have good space-filling properties. The designs are based on a general lattice structure that will also enable investigation of standard modeling approaches for computer experiments. The anticipated outcomes of this work will be practical methodology to be used in science and industry, as well as theoretical work that leads to changes in the manner in which computer experiments are conducted. The research addressed in this program is heavily motivated by problems arising from collaboration with scientists and engineers. All aspects of the proposed work include trainees.