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Global sensitivity analysis using complex linear models

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Abstract

A global sensitivity analysis of complex computer codes is usually performed by calculating the Sobol indices. The indices are estimated using Monte Carlo methods. The Monte Carlo simulations are time-consuming even if the computer response is replaced by a metamodel. This paper proposes a new method for calculating sensitivity indices that overcomes the Monte Carlo estimation. The method assumes a discretization of the domain of simulation and uses the expansion of the computer response on an orthogonal basis of complex functions to built a metamodel. This metamodel is then used to derive an analytical estimation of the Sobol indices. This approach is successfully tested on analytical functions and is compared with two alternative methods.

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References

  • Bailey, R.A.: Factorial designs and abelian groups. Linear Algebra Appl. 70, 349–363 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  • Bates, R.A., Buck, R.J., Riccomagno, E., Wynn, H.P.: Experimental design and observation for large systems. J. R. Stat. Soc. B 58, 77–94 (1996)

    MathSciNet  MATH  Google Scholar 

  • Bates, R.A., Riccomagno, E., Schwabe, R., Wynn, H.P.: Lattices and dual lattices in optimal experimental design for Fourier models. Comput. Stat. Data Anal. 28, 283–296 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • Fang, K.T., Li, R., Sudjianto, A.: Design and Modeling for Computer Experiments. Chapman & Hall, London (2006)

    MATH  Google Scholar 

  • Husslage, B., Rennen, G., van Dam, E., den Hertog, D.: Space-filling Latin hypercube designs for computer experiments. CentER Discussion Paper 2008-104. Tilburg University (2008)

  • Johnson, M.E., Moore, L.M., Ylvisaker, D.: Minimax and maximin distance design. J. Stat. Plan. Inference 26, 131–148 (1990)

    Article  MathSciNet  Google Scholar 

  • Kobilinsky, A.: Complex linear models and cyclic designs. Linear Algebra Appl. 127, 227–282 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  • Niederreiter, H.: Random number generation and quasi-Monte Carlo methods. Technical Report no4. CBMS-NSF, SIAM, Philadelphia, Illinois, Dept. of Statistics (1992)

  • Riccomagno, E., Schwabe, R., Wynn, H.P.: Lattice-based D-optimum design for Fourier regression. Ann. Stat. 25, 2313–2327 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4, 409–435 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  • Saltelli, A., Tarantola, S., Chan, K.: A quantitative, model independent method for global sensitivity analysis of model output. Technometrics 41, 39–56 (1999)

    Article  Google Scholar 

  • Saltelli, A., Chan, K., Scott, M. (eds.): Sensitivity Analysis. Wiley Series in Probability and Statistics. Wiley, New York (2000)

    MATH  Google Scholar 

  • Santner, T.J., Williams, B.J., Notz, W.I.: The Design and Analysis of Computer Experiments. Springer Series in Statistics. Springer, New York (2003)

    MATH  Google Scholar 

  • Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55, 271–280 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliab. Eng. Syst. Saf. 93, 964–979 (2008)

    Article  Google Scholar 

Download references

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  1. Département de Mathématiques, E.I.S.T.I., 26 avenue des Lilas, 64062, Pau cedex 9, France

    Astrid Jourdan

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  1. Astrid Jourdan
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Correspondence to Astrid Jourdan.

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Jourdan, A. Global sensitivity analysis using complex linear models. Stat Comput 22, 823–831 (2012). https://doi.org/10.1007/s11222-011-9239-y

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  • DOI: https://doi.org/10.1007/s11222-011-9239-y

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