Noncollapsing Space-Filling Designs for Bounded Nonrectangular Regions

Abstract

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.

Keywords:

• Average reciprocal distance
• Column-wise algorithm
• Computer experiment
• High-dimensional input space
• Maximin design.

Supplementary materials

The supplemental materials for this paper include, firstly, a pure R code implemention of concad using ARD and MIPD and also an R/C version of concad that employes a C version of the ARD algorithm. Secondly, these materials include the MIPD and ARD values from 3 * 24 concad runs using all 24 different permutations of inputs for the example in Section 5 for three selections of α, 0.0, 0.5, and 1.0. Thirdly, the materials provide comparisons of the MIPD and ARD values for concad generated designs for a set of rectangular input cases with the MIPD values for designs known to be Maximin. Lastly, the supplemental materials provide a study of the designs that concad produces for a sequence of increasingly thin, wedge-shaped regions.