Design for Sequential Follow-Up Experiments in Computer Emulations

ABSTRACT

Sequential experiments composed of initial experiments and follow-up experiments are widely adopted for economical computer emulations. Many kinds of Latin hypercube designs with good space-filling properties have been proposed for designing the initial computer experiments. However, little work based on Latin hypercubes has focused on the design of the follow-up experiments. Although some constructions of nested Latin hypercube designs can be adapted to sequential designs, the size of the follow-up experiments needs to be a multiple of that of the initial experiments. In this article, a general method for constructing sequential designs of flexible size is proposed, which allows the combined designs to have good one-dimensional space-filling properties. Moreover, the sampling properties and a type of central limit theorem are derived for these designs. Several improvements of these designs are made to achieve better space-filling properties. Simulations are carried out to verify the theoretical results. Supplementary materials for this article are available online.

KEYWORDS:

• Central limit theorem
• Computer experiment
• Latin hypercube design
• Sampling property
• Sequential design

Supplementary Materials

The online appendices include sampling properties of SDs, proofs of theorems, and additional figures.

Acknowledgments

All authors thank the editor, associate editor, and two referees for their valuable comments and insightful suggestions that helped us improve the presentation of this article. Ai's work is supported by NSFC grants 11331011 and 11671019, BCMIIS and LMEQF. Tsui's work is supported by NSFC grant 11471275 and the Hong Kong Research Grant Council No. T32-101/15-R.