Different numerical estimators for main effect global sensitivity indices

The variance-based method of global sensitivity indices based on Sobol sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol indices generally requires a large number of function evaluations to achieve reasonable convergence. Four different direct formulas for computing Sobol main effect sensitivity indices are compared on a set of test problems for which there are analytical results. These formulas are based on high-dimensional integrals which are evaluated using MC and QMC techniques. Direct formulas are also compared with a different approach based on the so-called double loop reordering formula. It is found that the double loop reordering (DLR) approach shows a superior performance among all methods both for models with independent and dependent variables.

[1]  Olivier Roustant,et al.  Calculations of Sobol indices for the Gaussian process metamodel , 2008, Reliab. Eng. Syst. Saf..

[2]  Paola Annoni,et al.  Estimation of global sensitivity indices for models with dependent variables , 2012, Comput. Phys. Commun..

[3]  Nilay Shah,et al.  The identification of model effective dimensions using global sensitivity analysis , 2011, Reliab. Eng. Syst. Saf..

[4]  Stefano Tarantola,et al.  Sensitivity Analysis in Practice , 2002 .

[5]  Ilya M. Sobol,et al.  Sensitivity Estimates for Nonlinear Mathematical Models , 1993 .

[6]  Kristin Isaacs,et al.  Estimating Sobol sensitivity indices using correlations , 2012, Environ. Model. Softw..

[7]  Stefano Tarantola,et al.  Application of the control variate technique to estimation of total sensitivity indices , 2015, Reliab. Eng. Syst. Saf..

[8]  Jim W. Hall,et al.  Sensitivity analysis of environmental models: A systematic review with practical workflow , 2014, Environ. Model. Softw..

[9]  Art B. Owen,et al.  Better estimation of small sobol' sensitivity indices , 2012, TOMC.

[10]  Nilay Shah,et al.  Metamodelling with independent and dependent inputs , 2013, Comput. Phys. Commun..

[11]  Paola Annoni,et al.  Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , 2010, Comput. Phys. Commun..

[12]  I. Sobol.  Uniformly distributed sequences with an additional uniform property , 1976 .

[13]  Stefano Tarantola,et al.  Random balance designs for the estimation of first order global sensitivity indices , 2006, Reliab. Eng. Syst. Saf..

[14]  Stefano Tarantola,et al.  Estimating the approximation error when fixing unessential factors in global sensitivity analysis , 2007, Reliab. Eng. Syst. Saf..

[15]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[16]  E. E. Myshetskaya,et al.  Monte Carlo estimators for small sensitivity indices , 2008, Monte Carlo Methods Appl..

[17]  A. Saltelli,et al.  Making best use of model evaluations to compute sensitivity indices , 2002 .

[18]  Elmar Plischke,et al.  An effective algorithm for computing global sensitivity indices (EASI) , 2010, Reliab. Eng. Syst. Saf..

[19]  I. Sobol.  Global Sensitivity Indices for Nonlinear Mathematical Models , 2004 .

[20]  D. Shahsavani,et al.  Variance-based sensitivity analysis of model outputs using surrogate models , 2011, Environ. Model. Softw..

[21]  I. Sobol,et al.  Construction and Comparison of High-Dimensional Sobol' Generators , 2011 .

[22]  Bruno Sudret,et al.  Adaptive sparse polynomial chaos expansion based on least angle regression , 2011, J. Comput. Phys..

[23]  Kwang-Il Ahn,et al.  A new approach for measuring uncertainty importance and distributional sensitivity in probabilistic safety assessment , 1994 .

[24]  Elmar Plischke,et al.  An adaptive correlation ratio method using the cumulative sum of the reordered output , 2012, Reliab. Eng. Syst. Saf..

[25]  I. Sobol,et al.  Global sensitivity indices for nonlinear mathematical models. Review , 2005 .

[26]  T. Klein,et al.  Asymptotic normality and efficiency of two Sobol index estimators , 2013, 1303.6451.