Weighted space-filling designs

Abstract

Many computer models or simulators have probabilistic dependencies between their input variables, which if not accounted for during design selection may result in a large numbers of simulator runs being required for analysis. We propose a method that incorporates known dependencies between input variables into design selection for simulators and demonstrate the benefits of this approach via a simulator for atmospheric dispersion. We quantify the benefit of the new techniques over standard space-filling and Monte Carlo simulation. The proposed methods are adaptations of computer-generated spread and coverage space-filling designs, with ‘distance’ between two input points redefined to include a weight function. This weight function reflects any known multivariate dependencies between input variables and prior information on the design region. The methods can include quantitative and qualitative variables, and different types of prior information. Novel graphical methods, adapted from fraction of design space plots, are used to assess and compare the designs.

Keywords:

• computer experiments
• defence studies
• design of experiments
• simulation experiments

Acknowledgements

This work was funded by the Defense Threat Reduction Agency and the Ministry of Defence Research Acquisitions Office; VEB was supported by a Dstl Associate Fellowship and DCW was partly supported by a Fellowship from the UK Engineering and Physical Sciences Research Council. We are grateful to Susan Lewis (University of Southampton), and Steven Taylor, Douglas Strickland and Thomas Graham (Dstl) for discussions and assistance. We also thank two referees whose comments improved the paper.© Crown copyright 2013. Published with the permission of the Defence Science and Technology Laboratory on behalf of the Controller of Her Majesty's Stationary Office.