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Uniform design over general input domains with applications to target region estimation in computer experiments

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  • Chuang, S.C.
  • Hung, Y.C.

Abstract

The power of uniform design (UD) has received great attention in the area of computer experiments over the last two decades. However, when conducting a typical computer experiment, one finds many non-rectangular types of input domains on which traditional UD methods cannot be adequately applied. In this study, we propose a new UD method that is suitable for any type of design area. For practical implementation, we develop an efficient algorithm to construct a so-called nearly uniform design (NUD) and show that it approximates very well the UD solution for small sizes of experiment. By utilizing the proposed UD method, we also develop a methodology for estimating the target region of computer experiments. The methodology is sequential and aims to (i) provide adaptive models that predict well the output measures related to the experimental target; and (ii) minimize the number of experimental trials. Finally, we illustrate the developed methodology on various examples and show that, given the same experimental budget, it outperforms other approaches in estimating the prespecified target region of computer experiments.

Suggested Citation

  • Chuang, S.C. & Hung, Y.C., 2010. "Uniform design over general input domains with applications to target region estimation in computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 219-232, January.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:1:p:219-232
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    References listed on IDEAS

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    1. Huang, Chien-Ming & Lee, Yuh-Jye & Lin, Dennis K.J. & Huang, Su-Yun, 2007. "Model selection for support vector machines via uniform design," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 335-346, September.
    2. Fang, Kai-Tai & Qin, Hong, 2003. "A note on construction of nearly uniform designs with large number of runs," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 215-224, January.
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    Cited by:

    1. Lin, D.K.J. & Sharpe, C. & Winker, P., 2010. "Optimized U-type designs on flexible regions," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1505-1515, June.
    2. Chen, Ray-Bing & Hsu, Yen-Wen & Hung, Ying & Wang, Weichung, 2014. "Discrete particle swarm optimization for constructing uniform design on irregular regions," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 282-297.
    3. Zhang, Mei & Zhou, Yong-Dao, 2016. "Spherical discrepancy for designs on hyperspheres," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 226-234.
    4. Xiong, Zikang & Liu, Liwei & Ning, Jianhui & Qin, Hong, 2020. "Sphere packing design for experiments with mixtures," Statistics & Probability Letters, Elsevier, vol. 164(C).
    5. Ray-Bing Chen & Ying-Chao Hung & Weichung Wang & Sung-Wei Yen, 2013. "Contour estimation via two fidelity computer simulators under limited resources," Computational Statistics, Springer, vol. 28(4), pages 1813-1834, August.

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