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The generalization of Latin hypercube sampling

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  • Shields, Michael D.
  • Zhang, Jiaxin

Abstract

Latin hypercube sampling (LHS) is generalized in terms of a spectrum of stratified sampling (SS) designs referred to as partially stratified sample (PSS) designs. True SS and LHS are shown to represent the extremes of the PSS spectrum. The variance of PSS estimates is derived along with some asymptotic properties. PSS designs are shown to reduce variance associated with variable interactions, whereas LHS reduces variance associated with main effects. Challenges associated with the use of PSS designs and their limitations are discussed. To overcome these challenges, the PSS method is coupled with a new method called Latinized stratified sampling (LSS) that produces sample sets that are simultaneously SS and LHS. The LSS method is equivalent to an Orthogonal Array based LHS under certain conditions but is easier to obtain. Utilizing an LSS on the subspaces of a PSS provides a sampling strategy that reduces variance associated with both main effects and variable interactions and can be designed specially to minimize variance for a given problem. Several high-dimensional numerical examples highlight the strengths and limitations of the method. The Latinized partially stratified sampling method is then applied to identify the best sample strategy for uncertainty quantification on a plate buckling problem.

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  • Shields, Michael D. & Zhang, Jiaxin, 2016. "The generalization of Latin hypercube sampling," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 96-108.
    • Handle: RePEc:eee:reensy:v:148:y:2016:i:c:p:96-108
    DOI: 10.1016/j.ress.2015.12.002
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    1. Alger Ingela & Ma Ching-to Albert & Renault Regis, 2012. "Experience Benefits and Firm Organization," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-35, September.
    2. 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.
    3. Marco Ratto, 2008. "Analysing DSGE Models with Global Sensitivity Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 115-139, March.
    4. Michael D. Shields & V.S. Sundar, 2015. "Targeted random sampling: a new approach for efficient reliability estimation for complex systems," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 9(2/3), pages 174-190.
    5. Helton, J.C. & Johnson, J.D. & Sallaberry, C.J. & Storlie, C.B., 2006. "Survey of sampling-based methods for uncertainty and sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1175-1209.
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