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Nested Maximum Entropy Designs for Computer Experiments

Author

Listed:
  • Weiyan Mu

    (School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China)

  • Chengxin Liu

    (School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China)

  • Shifeng Xiong

    (NCMIS, KLSC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China)

Abstract

Presently, computer experiments with multiple levels of accuracy are widely applied in science and engineering. This paper introduces a class of nested maximum entropy designs for such computer experiments. A multi-layer DETMAX algorithm is proposed to construct nested maximum entropy designs. Based on nested maximum entropy designs, we also propose an integer-programming procedure to specify the sample sizes in multi-fidelity computer experiments. Simulated annealing techniques are used to tackle complex optimization problems in the proposed methods. Illustrative examples show that the proposed nested entropy designs can yield better prediction results than nested Latin hypercube designs in the literature and that the proposed sample-size determination method is effective.

Suggested Citation

  • Weiyan Mu & Chengxin Liu & Shifeng Xiong, 2023. "Nested Maximum Entropy Designs for Computer Experiments," Mathematics, MDPI, vol. 11(16), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3572-:d:1219611
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    References listed on IDEAS

    as
    1. Yunfei Wei & Shifeng Xiong, 2019. "Bayesian integrative analysis for multi-fidelity computer experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(11), pages 1973-1987, August.
    2. Sukanta Dash & Baidya Nath Mandal & Rajender Parsad, 2020. "On the construction of nested orthogonal Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 347-353, April.
    3. Rennen, G. & Husslage, B.G.M. & van Dam, E.R. & den Hertog, D., 2009. "Nested Maximin Latin Hypercube Designs," Discussion Paper 2009-06, Tilburg University, Center for Economic Research.
    4. Bing Guo & Xue-Ping Chen & Min-Qian Liu, 2020. "Construction of Latin hypercube designs with nested and sliced structures," Statistical Papers, Springer, vol. 61(2), pages 727-740, April.
    5. Mu, Weiyan & Xiong, Shifeng, 2018. "A class of space-filling designs and their projection properties," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 129-134.
    6. Cox, Dennis D. & Park, Jeong-Soo & Singer, Clifford E., 2001. "A statistical method for tuning a computer code to a data base," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 77-92, July.
    7. Yaping Wang & Fasheng Sun & Hongquan Xu, 2022. "On Design Orthogonality, Maximin Distance, and Projection Uniformity for Computer Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 375-385, January.
    8. Xu, Jin & Duan, Xiaojun & Wang, Zhengming & Yan, Liang, 2018. "A general construction for nested Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 134-140.
    9. Weiyan Mu & Qiuyue Wei & Dongli Cui & Shifeng Xiong, 2018. "Best Linear Unbiased Prediction for Multifidelity Computer Experiments," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-7, June.
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