Asymmetric Nested Lattice Samples
Peter Z. G. Qian1, Mingyao Ai2;3, Youngdeok Hwang1 and Heng Su4
1 Department of Statistics, University of Wisconsin-Madison, Madison, WI 53706
2 LMAM, School of Mathematical Sciences and Center for Statistical Science
Peking University, Beijing 100871, China
3 Corresponding author
4 H. Milton Stewart School of Industrial and Systems Engineering,
Georgia Institute of Technology, Atlanta, GA 30332, USA
KEY WORDS: Computer experiment; Design of experiments; Asymmetric orthogonal ar-
ray; Orthogonal array based Latin hypercube; Sequential design; Space-ˉlling design; Ran-
domized orthogonal array.
AbstractWe propose an approach for constructing a new class of space-ˉlling designs, calledasymmetric nested lattice samples. As a stepping-stone to the proposed approach, weintroduce two methods for generating asymmetric nested orthogonal arrays. We thenpresent two elaborate randomization methods to shu2e the levels of an asymmetricnested orthogonal array to produce a pair of asymmetric nested lattice samples. Theconstructed designs have a desirable nested structure, possess attractive space-ˉllingproperties and allow di®erent axes to be divided at di®erent scales of ˉneness. Formulti-ˉdelity computer experiments, sequential evaluations, multi-step functional ˉt-ting and linking parameters, the asymmetric feature is appealing for situations wheresome factors are believed to be more important or deserve more attention than theother factors. The proposed designs are also useful for problems in these applicationswhere di®erent factors, by nature, require dividing their axes at di®erent levels ofˉnesse.1

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