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Hierarchical Latin Hypercube Sampling

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  • Vikram V. Garg
  • Roy H. Stogner

Abstract

Latin hypercube sampling (LHS) is a robust, scalable Monte Carlo method that is used in many areas of science and engineering. We present a new algorithm for generating hierarchic Latin hypercube sets (HLHS) that are recursively divisible into LHS subsets. Based on this new construction, we introduce a hierarchical incremental LHS (HILHS) method that allows the user to employ LHS in a flexibly incremental setting. This overcomes a drawback of many LHS schemes that require the entire sample set to be selected a priori, or only allow very large increments. We derive the sampling properties for HLHS designs and HILHS estimators. We also present numerical studies that showcase the flexible incrementation offered by HILHS.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:518:p:673-682
    DOI: 10.1080/01621459.2016.1158717
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    References listed on IDEAS

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    1. 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.
    2. Peter Z. G. Qian, 2009. "Nested Latin hypercube designs," Biometrika, Biometrika Trust, vol. 96(4), pages 957-970.
    3. 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.
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    Cited by:

    1. Bing Guo & Xiao-Rong Li & Min-Qian Liu & Xue Yang, 2023. "Construction of orthogonal general sliced Latin hypercube designs," Statistical Papers, Springer, vol. 64(3), pages 987-1014, June.

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