A NEW AND FLEXIBLE METHOD FOR CONSTRUCTING DESIGNS FOR COMPUTER EXPERIMENTS

Chunfang Devon Lin · Derek Bingham

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Optimal Experimental Design Methods Advanced Combinatorial Mathematics Mathematical Approximation and Integration

Abstract

We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of orthogonal Latin hypercubes and obtain many results along the way. In terms of run sizes, the existence problem of orthogonal Latin hypercubes is completely solved. We also present an explicit result showing how large orthogonal Latin hypercubes can be constructed using small orthogonal Latin hypercubes. Another appealing feature of our method is that it can easily be adapted to construct other designs; we examine how to make use of the method to construct nearly orthogonal and cascading Latin hypercubes.

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References

2000A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code 1989Design and Analysis of Computer Experiments 1995Exploratory designs for computational experiments 1992Screening, Predicting, and Computer Experiments 1987Maximum entropy sampling 1998Orthogonal Column Latin Hypercubes and Their Application in Computer Experiments 2007Efficient Nearly Orthogonal and Space-Filling Latin Hypercubes 1999Fractional Factorial Plans

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2011Accurate emulators for large-scale computer experiments 2011Construction of orthogonal and nearly orthogonal latin hypercube designs from orthogonal designs 2020On Design Orthogonality, Maximin Distance, and Projection Uniformity for Computer Experiments 2014Engineering-Driven Statistical Adjustment and Calibration 2014Design for computer experiments with qualitative and quantitative factors 2016A Method of Constructing Space-Filling Orthogonal Designs

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