Sequentially Refined Latin Hypercube Designs: Reusing Every Point

Abstract

The use of iteratively enlarged Latin hypercube designs for running computer experiments has recently gained popularity in practice. This approach conducts an initial experiment with a computer code using a Latin hypercube design and then runs a follow-up experiment with additional runs elaborately chosen so that the combined design set for the two experiments forms a larger Latin hypercube design. This augmenting process can be repeated multiple stages, where in each stage the augmented design set is guaranteed to be a Latin hypercube design. We provide a theoretical framework to put this approach on a firm footing. Numerical examples are given to corroborate the derived theoretical results. Supplementary materials for this article are available online.

• Computer experiments
• Design of experiments
• Numerical integration
• Sequential evaluation

Additional information

Notes on contributors

Jin Xu

Jin Xu is Professor, Department of Statistics and Actuarial Science, East China Normal University, 500 Dongchuan Road, Shanghai, 200241, China (E-mail: [email protected]). Jiajie Chen is Quantitative Associate, Wells Fargo, Charlotte, NC 28202 (E-mail: [email protected]). Peter Z. G. Qian is Professor, Department of Statistics, University of Wisconsin-Madison, Medical Science Center, WI 53706 (E-mail: [email protected]). Xu is supported by the National Natural Science Foundation of China Grant 11271134. Chen and Qian are supported by the U.S. National Science Foundation Grant 1055214. The authors thank the editor, the associate editor and referees for their useful comments, which have led to improvements of the paper.

Jiajie Chen

Jin Xu is Professor, Department of Statistics and Actuarial Science, East China Normal University, 500 Dongchuan Road, Shanghai, 200241, China (E-mail: [email protected]). Jiajie Chen is Quantitative Associate, Wells Fargo, Charlotte, NC 28202 (E-mail: [email protected]). Peter Z. G. Qian is Professor, Department of Statistics, University of Wisconsin-Madison, Medical Science Center, WI 53706 (E-mail: [email protected]). Xu is supported by the National Natural Science Foundation of China Grant 11271134. Chen and Qian are supported by the U.S. National Science Foundation Grant 1055214. The authors thank the editor, the associate editor and referees for their useful comments, which have led to improvements of the paper.

Peter Z. G. Qian

Jin Xu is Professor, Department of Statistics and Actuarial Science, East China Normal University, 500 Dongchuan Road, Shanghai, 200241, China (E-mail: [email protected]). Jiajie Chen is Quantitative Associate, Wells Fargo, Charlotte, NC 28202 (E-mail: [email protected]). Peter Z. G. Qian is Professor, Department of Statistics, University of Wisconsin-Madison, Medical Science Center, WI 53706 (E-mail: [email protected]). Xu is supported by the National Natural Science Foundation of China Grant 11271134. Chen and Qian are supported by the U.S. National Science Foundation Grant 1055214. The authors thank the editor, the associate editor and referees for their useful comments, which have led to improvements of the paper.