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Further results on orthogonal arrays for the estimation of global sensitivity indices based on alias matrix

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Listed:
  • Xue-ping Chen
  • Jin-Guan Lin
  • Xiao-di Wang
  • Xing-fang Huang

Abstract

In this paper, the use of orthogonal arrays with strength $$s>p,$$ s > p , where $$p$$ p is the required strength, for global sensitivity analysis is considered. We first generalize the alias matrix for ANOVA high-dimensional model representation based on matrix image, and then by sequentially minimizing the squared alias degrees, we present a approach for the estimation of sensitivity indices. A two-level orthogonal array with 16 runs and a four-level orthogonal array with 64 runs are studied for estimating both low-order and high-order significant sensitivity indices. Moreover, models containing larger than 10 input factors are also investigated. All cases show that designs with smaller squared alias degree have less bias and variance for the estimations of global sensitivity indices. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Xue-ping Chen & Jin-Guan Lin & Xiao-di Wang & Xing-fang Huang, 2015. "Further results on orthogonal arrays for the estimation of global sensitivity indices based on alias matrix," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 411-426, September.
    • Handle: RePEc:spr:stmapp:v:24:y:2015:i:3:p:411-426
    DOI: 10.1007/s10260-014-0290-7
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    References listed on IDEAS

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    1. Dimov, I. & Georgieva, R., 2010. "Monte Carlo algorithms for evaluating Sobol’ sensitivity indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 506-514.
    2. Pang, Shanqi & Zhang, Yingshan & Liu, Sanyang, 2004. "Further results on the orthogonal arrays obtained by generalized Hadamard product," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 17-25, June.
    3. Tarantola, S. & Gatelli, D. & Mara, T.A., 2006. "Random balance designs for the estimation of first order global sensitivity indices," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 717-727.
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