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Sliced Latin Hypercube Designs

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  • Peter Z. G. Qian

Abstract

This article proposes a method for constructing a new type of space-filling design, called a sliced Latin hypercube design, intended for running computer experiments. Such a design is a special Latin hypercube design that can be partitioned into slices of smaller Latin hypercube designs. It is desirable to use the constructed designs for collective evaluations of computer models and ensembles of multiple computer models. The proposed construction method is easy to implement, capable of accommodating any number of factors, and flexible in run size. Examples are given to illustrate the method. Sampling properties of the constructed designs are examined. Numerical illustration is provided to corroborate the derived theoretical results.

Suggested Citation

  • Peter Z. G. Qian, 2012. "Sliced Latin Hypercube Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 393-399, March.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:393-399
    DOI: 10.1080/01621459.2011.644132
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    Cited by:

    1. Wang, Sumin & Wang, Dongying & Sun, Fasheng, 2019. "A central limit theorem for marginally coupled designs," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 168-174.
    2. Chen, Hao & Yang, Jinyu & Lin, Dennis K.J. & Liu, Min-Qian, 2019. "Sliced Latin hypercube designs with both branching and nested factors," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 124-131.
    3. Wang, Xiao-Lei & Zhao, Yu-Na & Yang, Jian-Feng & Liu, Min-Qian, 2017. "Construction of (nearly) orthogonal sliced Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 174-180.
    4. Weiping Zhou & Jinyu Yang & Min-Qian Liu, 2021. "Construction of orthogonal marginally coupled designs," Statistical Papers, Springer, vol. 62(4), pages 1795-1820, August.
    5. Yang You & Guang Jin & Zhengqiang Pan & Rui Guo, 2021. "MP-CE Method for Space-Filling Design in Constrained Space with Multiple Types of Factors," Mathematics, MDPI, vol. 9(24), pages 1-13, December.
    6. Li, Min & Liu, Min-Qian & Wang, Xiao-Lei & Zhou, Yong-Dao, 2020. "Prediction for computer experiments with both quantitative and qualitative factors," Statistics & Probability Letters, Elsevier, vol. 165(C).
    7. Jing Zhang & Jin Xu & Kai Jia & Yimin Yin & Zhengming Wang, 2019. "Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes," Mathematics, MDPI, vol. 7(9), pages 1-16, September.
    8. Yang, Xue & Chen, Hao & Liu, Min-Qian, 2014. "Resolvable orthogonal array-based uniform sliced Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 108-115.
    9. Ray, Douglas & Ramirez-Marquez, Jose, 2020. "A framework for probabilistic model-based engineering and data synthesis," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    10. Zeng, Yaohui & Zhang, Zijun & Kusiak, Andrew, 2015. "Predictive modeling and optimization of a multi-zone HVAC system with data mining and firefly algorithms," Energy, Elsevier, vol. 86(C), pages 393-402.
    11. Vikram V. Garg & Roy H. Stogner, 2017. "Hierarchical Latin Hypercube Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 673-682, April.
    12. Xiangshun Kong & Mingyao Ai & Kwok Leung Tsui, 2018. "Flexible sliced designs for computer experiments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 631-646, June.
    13. Ru Yuan & Bing Guo & Min-Qian Liu, 2021. "Flexible sliced Latin hypercube designs with slices of different sizes," Statistical Papers, Springer, vol. 62(3), pages 1117-1134, June.

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