Many researchers use computer simulators as experimental tools, especially when physical experiments are infeasible. When computer codes are computationally intensive, nonparametric predictors can be fitted to training data for detailed exploration of the input-output relationship. The accuracy of such flexible predictors is enhanced by taking training inputs to be "space-filling." If there are inputs that have little or no effect on the response, it is desirable that the design be "noncollapsing" in the sense of having spacefilling lower dimensional projections. This article describes an algorithm for constructing noncollapsing space-filling designs for bounded input regions that are of possibly high dimension. Online supplementary materials provide the code for the algorithm, examples of its use, and show its performance in multiple settings.
Sophisticated computer codes that implement mathematical models of physical processes can involve large numbers of inputs, and screening to determine the most active inputs is critical for understanding the inputoutput relationship. This article presents a new two-stage group screening methodology for identifying active inputs. In Stage 1, groups of inputs showing low activity are screened out; in Stage 2, individual inputs from the active groups are identified. Inputs are evaluated through their estimated total (effect) sensitivity indices (TSIs), which are compared with a benchmark null TSI distribution created from added low noise inputs. Examples show that, compared with other procedures, the proposed method provides more consistent and accurate results for high-dimensional screening. Additional details and computer code are provided in supplementary materials available online.
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