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A-optimal designs for non-parametric symmetrical global sensitivity analysis

Author

Listed:
  • Xueping Chen

    (Jiangsu University of Technology)

  • Yujie Gai

    (Central University of Finance and Economics)

  • Xiaodi Wang

    (Central University of Finance and Economics)

Abstract

In the early stage of exploring a complex system, a preliminary experiment is used to capture the key characteristics of the model. Symmetrical global sensitivity analysis (SGSA) is one such experiment that explores the symmetrical structure of model by decomposing the model into independent symmetric functions. However, the existing experimental plans for SGSA rely on deterministic computational models that produce unique values of outputs when executed for specific values of inputs. In this paper, the problem of designing experiments for non-parametric SGSA is considered. Here the phrase “non-parametric” refers to model outputs containing random errors. The main result in the paper shows that a symmetrical design with certain constraints achieves A-optimum for the estimation of each output element function, and guarantees the superiority of the SGSA result. The statistical properties of non-parametric SGSA based on the optimal designs are further discussed, showing that the non-influential sensitivity indices can be estimated with low bias and volatility. Two explicit structures of the optimal designs are obtained. The optimality of the derived design is validated by simulation in the end.

Suggested Citation

  • Xueping Chen & Yujie Gai & Xiaodi Wang, 2023. "A-optimal designs for non-parametric symmetrical global sensitivity analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(2), pages 219-237, February.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:2:d:10.1007_s00184-022-00872-3
    DOI: 10.1007/s00184-022-00872-3
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    References listed on IDEAS

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    1. Jeremy E. Oakley & Anthony O'Hagan, 2004. "Probabilistic sensitivity analysis of complex models: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 751-769, August.
    2. Daniel Harenberg & Stefano Marelli & Bruno Sudret & Viktor Winschel, 2019. "Uncertainty quantification and global sensitivity analysis for economic models," Quantitative Economics, Econometric Society, vol. 10(1), pages 1-41, January.
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