Screening in physical and computer experiments

In many disciplines, scientists frequently encounter situations in which they must identify the few factors which significantly affect the response among numerous potential factors. Quite often, the sheer magnitude of the problem renders traditional (fractional) factorial experiments infeasible due to the extremely large number of observations that would be needed to successfully determine the active factors. Under the assumption of factor sparsity (where only a few of the many factors are active), another way of dealing with such a situation is to perform a screening experiment. The goal of a screening experiment is to sift through the large number of effects via designed experiments to separate the active from the inactive effects. Follow-up experiments can then be performed with only the small number of factors to fit a predictive model.;This dissertation addresses screening issues encountered in physical as well as in computer experiments. In physical experiments, in order to reduce the cost of experimentation, supersaturated designs are employed. Supersaturated designs are designs in which the number of observations is smaller than the number of factors under investigation. This dissertation proposes a way of constructing supersaturated designs. The particular structure of the constructed designs allows for easy examination of the properties of these designs. Then, in an extensive study, multiple analysis methods for screening experiments are compared in their ability to correctly classify factors as either active or inactive.;In some situations, it is economically, morally, or temporally not feasible to run a comprehensive physical experiment. However, it might be feasible to conduct a computer experiment. If the physical process can be described by a mathematical model which can be implemented as a computer code and the methods exist for solving this model in finite time, then one can run the computer code to produce a "response" at any combination of values of the inputs. In other words, one can conduct a computer experiment. This dissertation proposes an algorithm for constructing experimental designs suitable for computer experiments when the experimental region is a constrained polytope. These designs are particularly suitable for screening in computer experiments where the assumption is that only a subset of input variables significantly affects the response.