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Smoothing spline analysis of variance approach for global sensitivity analysis of computer codes

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  • Touzani, Samir
  • Busby, Daniel

Abstract

The paper investigates a nonparametric regression method based on smoothing spline analysis of variance (ANOVA) approach to address the problem of global sensitivity analysis (GSA) of complex and computationally demanding computer codes. The two steps algorithm of this method involves an estimation procedure and a variable selection. The latter can become computationally demanding when dealing with high dimensional problems. Thus, we proposed a new algorithm based on Landweber iterations. Using the fact that the considered regression method is based on ANOVA decomposition, we introduced a new direct method for computing sensitivity indices. Numerical tests performed on several analytical examples and on an application from petroleum reservoir engineering showed that the method gives competitive results compared to a more standard Gaussian process approach.

Suggested Citation

  • Touzani, Samir & Busby, Daniel, 2013. "Smoothing spline analysis of variance approach for global sensitivity analysis of computer codes," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 67-81.
    • Handle: RePEc:eee:reensy:v:112:y:2013:i:c:p:67-81
    DOI: 10.1016/j.ress.2012.11.008
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    References listed on IDEAS

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    1. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Description of techniques," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 28-54.
    2. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    3. Gramacy, Robert B & Lee, Herbert K. H, 2008. "Bayesian Treed Gaussian Process Models With an Application to Computer Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1119-1130.
    4. Ming Yuan & Yi Lin, 2007. "On the non‐negative garrotte estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 143-161, April.
    5. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Example results," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 55-77.
    6. Blatman, Géraud & Sudret, Bruno, 2010. "Efficient computation of global sensitivity indices using sparse polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1216-1229.
    7. Storlie, Curtis B. & Swiler, Laura P. & Helton, Jon C. & Sallaberry, Cedric J., 2009. "Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1735-1763.
    8. Marrel, Amandine & Iooss, Bertrand & Van Dorpe, François & Volkova, Elena, 2008. "An efficient methodology for modeling complex computer codes with Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4731-4744, June.
    9. 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.
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