Noncollapsing Space-Filling Designs for Bounded Nonrectangular Regions

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 space-filling 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.