Mathematical Sciences: Model Robust Design and Inference

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This research will be on experimental designs in settings where systematic departures from exact linear models are allowed but controlled. The study of design problems in dimensions higher than one is facilitated greatly by controlling the departure through the use of a stochastic process prior. Problems with and without measurement error are of interest. Important and interesting problems fitting the latter case arise in numerical integration and in the selection of inputs to computer model experiments and simulations. Algorithms for computing designs are to be devised, studied, and compared. Prediction of linear designs are to be devised, studied and compared. Prediction of linear functionals of the underlying regression or process will be emphasized; non-linear functionals bring added concerns also requiring study. The complexity of the problems and the necessity for addressing complex design spaces leads to the need and use of advanced computational resources. The primary goal of statistical experimental design is to assess the feasibility of a proposed experiment and to optimize the use of resources in the experiment. Most of current statistical theory applies to very simply configured experiments and analysis techniques. This is so because, until the computer revolution, the feasibility of experiments were severely limited by data collection and computational capabilities. This research is to broaden the theory of experimental design, to realistically apply to more modern scientific settings where technological advances are permitting more complex questions to be studied in controlled and controlled experiments.