Discrepancy measures for sensitivity analysis in mathematical modeling

While Sensitivity Analysis (SA) improves the transparency and reliability of mathematical models, its uptake by modelers is still scarce. This is partially explained by its technical requirements, which may be hard to decipher and interpret for the non-specialist. Here we draw on the concept of discrepancy and propose a sensitivity measure that is as easy to understand as the visual inspection of input-output scatterplots. Numerical experiments on classic SA functions and on meta-models suggest that the symmetric L 2 discrepancy measure is able to rank the most influential parameters almost as accurately as the variance-based total sensitivity index, one of the most established global sensitivity measures.

[1]  R. Rosati,et al.  A function dataset for benchmarking in sensitivity analysis , 2022, Data in brief.

[2]  William Becker,et al.  A comprehensive comparison of total-order estimators for global sensitivity analysis , 2020, International Journal for Uncertainty Quantification.

[3]  William Becker,et al.  Metafunctions for benchmarking in sensitivity analysis , 2020, Reliab. Eng. Syst. Saf..

[4]  Philip B. Stark,et al.  Five ways to ensure that models serve society: a manifesto , 2020, Nature.

[5]  A. Saltelli,et al.  Why so many published sensitivity analyses are false: A systematic review of sensitivity analysis practices , 2017, Environ. Model. Softw..

[6]  Saman Razavi,et al.  Global sensitivity analysis for high-dimensional problems: How to objectively group factors and measure robustness and convergence while reducing computational cost , 2019, Environ. Model. Softw..

[7]  Xiaobo Zhou,et al.  Global Sensitivity Analysis , 2017, Encyclopedia of GIS.

[8]  H. Gupta,et al.  A new framework for comprehensive, robust, and efficient global sensitivity analysis: 1. Theory , 2016 .

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

[10]  Art B. Owen,et al.  Sobol' Indices and Shapley Value , 2014, SIAM/ASA J. Uncertain. Quantification.

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

[12]  Paola Annoni,et al.  Sixth International Conference on Sensitivity Analysis of Model Output How to avoid a perfunctory sensitivity analysis , 2010 .

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

[14]  J. Franco.  Planification d'expériences numériques en phase exploratoire pour la simulation des phénomènes complexes , 2008 .

[15]  Andrea Saltelli,et al.  Sensitivity Analysis for Importance Assessment , 2002, Risk analysis : an official publication of the Society for Risk Analysis.

[16]  Yong Zhang,et al.  Uniform Design: Theory and Application , 2000, Technometrics.

[17]  M. Jansen.  Analysis of variance designs for model output , 1999 .

[18]  Fred J. Hickernell,et al.  A generalized discrepancy and quadrature error bound , 1998, Math. Comput..

[19]  A. Saltelli,et al.  Importance measures in global sensitivity analysis of nonlinear models , 1996 .

[20]  Harald Niederreiter,et al.  Implementation and tests of low-discrepancy sequences , 1992, TOMC.