Sliced Rotated Sphere Packing Designs

ABSTRACT

Space-filling designs are popular choices for computer experiments. A sliced design is a design that can be partitioned into several subdesigns. We propose a new type of sliced space-filling design called sliced rotated sphere packing designs. Their full designs and subdesigns are rotated sphere packing designs. They are constructed by rescaling, rotating, translating, and extracting the points from a sliced lattice. We provide two fast algorithms to generate such designs. Furthermore, we propose a strategy to use sliced rotated sphere packing designs adaptively. Under this strategy, initial runs are uniformly distributed in the design space, follow-up runs are added by incorporating information gained from initial runs, and the combined design is space-filling for any local region. Examples are given to illustrate its potential application.

KEYWORDS:

• Design of experiment
• Expected improvement
• Maximin distance
• Nested design
• Sequential design

Supplementary Materials

• Computer code: R code to generate sliced rotated sphere packing designs. (GNU zipped tar file)

Acknowledgments

The author thank the editor, an associate editor and two referees for their helpful comments and suggestions, which have led to improvements in the article. He is supported by funding from Chinese Ministry of Science and Technology (2016YFF0203801), Special National Key Research and Development Plan (2016YFD0400206), National Natural Science Foundation of China (NSFC 11501550, NSFC 11671386) and National Center for Mathematics and Interdisciplinary Sciences, CAS.

Additional information

Funding

National Natural Science Foundation of China(10.13039/501100001809, 11501550, 11671386), Special National Key Research and Development Plan(2016YFD0400206), Funding from Chinese Ministry of Science and Technology(2016YFF0203801)