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Sequentially Refined Latin Hypercube Designs: Reusing Every Point

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  • Jin Xu
  • Jiajie Chen
  • Peter Z. G. Qian

Abstract

The use of iteratively enlarged Latin hypercube designs for running computer experiments has recently gained popularity in practice. This approach conducts an initial experiment with a computer code using a Latin hypercube design and then runs a follow-up experiment with additional runs elaborately chosen so that the combined design set for the two experiments forms a larger Latin hypercube design. This augmenting process can be repeated multiple stages, where in each stage the augmented design set is guaranteed to be a Latin hypercube design. We provide a theoretical framework to put this approach on a firm footing. Numerical examples are given to corroborate the derived theoretical results. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:512:p:1696-1706
    DOI: 10.1080/01621459.2014.993078
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    References listed on IDEAS

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    1. 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.
    2. Xu He & Peter Z. G. Qian, 2011. "Nested orthogonal array-based Latin hypercube designs," Biometrika, Biometrika Trust, vol. 98(3), pages 721-731.
    3. Peter Z. G. Qian, 2009. "Nested Latin hypercube designs," Biometrika, Biometrika Trust, vol. 96(4), pages 957-970.
    4. Tong, Charles, 2006. "Refinement strategies for stratified sampling methods," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1257-1265.
    5. Sallaberry, C.J. & Helton, J.C. & Hora, S.C., 2008. "Extension of Latin hypercube samples with correlated variables," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 1047-1059.
    6. Rennen, G. & Husslage, B.G.M. & van Dam, E.R. & den Hertog, D., 2009. "Nested Maximin Latin Hypercube Designs," Other publications TiSEM 1c504ec0-f357-42d2-9c92-9, Tilburg University, School of Economics and Management.
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    Cited by:

    1. 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.

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