Design Methodology for Computer and Physical Experiments

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Statistical models provide powerful tools that enable researchers to investigate complex systems from almost every imaginable field of studies in natural sciences, engineering, social sciences and humanities. A crucial step in the process of model building is the data collection. No matter how elaborate and sophisticated a model building process is, a statistical model contains no more information than what the data can offer. Experimental design is an area of statistics devoted to the study of efficient methods for informative data collection and corresponding methods of data analysis. ****Fractional factorial designs are a class of experimental plans for exploring the relationship between a response variable and a set of explanatory variables. Their practical usefulness and theoretical importance are well documented in the literature. The first broad objective of this research proposal is to extend the existing methods and develop new methodology for fractional factorial designs. Two focal points of the proposed research are optimality and robustness. In particular, we will investigate optimality and robustness of fractional factorial designs under a recently developed baseline parametrization. ***Computer models are increasingly popular nowadays. When the computer code representing a computer model is expensive to run, it is desirable to build a cheaper surrogate model. Computer experiments are concerned with the building of a statistical surrogate model based on the data consisting of a set of carefully selected inputs and the corresponding outputs from running a computer code. Space-filling designs have been widely accepted as appropriate designs for computer experiments. The second broad objective of the proposed research is to consolidate the existing methods and develop new methods for constructing space-filling designs. Particular attention will be paid to two classes of space-filling designs, namely, strong orthogonal arrays and mappable nearly orthogonal arrays.***Training HQP and disseminating research results are two important aspects of the proposed research, which will be accomplished by involving students in research activities and by collaborating with statistical practitioners. Completion of the proposed research will shed new light on design theory, result in new designs for computer and physical experiments, and promote further applications of design methodology.*** *** **