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Nested Latin hypercube designs

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  • Peter Z. G. Qian

Abstract

We propose an approach to constructing nested Latin hypercube designs. Such designs are useful for conducting multiple computer experiments with different levels of accuracy. A nested Latin hypercube design with two layers is defined to be a special Latin hypercube design that contains a smaller Latin hypercube design as a subset. Our method is easy to implement and can accommodate any number of factors. We also extend this method to construct nested Latin hypercube designs with more than two layers. Illustrative examples are given. Some statistical properties of the constructed designs are derived. Copyright 2009, Oxford University Press.

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  • Peter Z. G. Qian, 2009. "Nested Latin hypercube designs," Biometrika, Biometrika Trust, vol. 96(4), pages 957-970.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:4:p:957-970
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    File URL: http://hdl.handle.net/10.1093/biomet/asp045
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    Citations

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    Cited by:

    1. 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.
    2. Crombecq, K. & Laermans, E. & Dhaene, T., 2011. "Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling," European Journal of Operational Research, Elsevier, vol. 214(3), pages 683-696, November.
    3. Jin Xu & Jiajie Chen & Peter Z. G. Qian, 2015. "Sequentially Refined Latin Hypercube Designs: Reusing Every Point," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1696-1706, December.
    4. Hao Chen & Yan Zhang & Xue Yang, 2021. "Uniform projection nested Latin hypercube designs," Statistical Papers, Springer, vol. 62(4), pages 2031-2045, August.
    5. Shields, Michael D. & Teferra, Kirubel & Hapij, Adam & Daddazio, Raymond P., 2015. "Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 310-325.
    6. 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.
    7. Sigal Levy & David Steinberg, 2010. "Computer experiments: a review," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(4), pages 311-324, December.
    8. 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.
    9. Chen, Xi & Zhou, Qiang, 2017. "Sequential design strategies for mean response surface metamodeling via stochastic kriging with adaptive exploration and exploitation," European Journal of Operational Research, Elsevier, vol. 262(2), pages 575-585.

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