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Sensitivity analysis with dependence and variance-based measures for spatio-temporal numerical simulators

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In a case of radioactive release in the environment, modeling the radionuclide atmospheric dispersion is particularly useful for emergency response procedures and risk assessment. For this, the CEA has developed a numerical simulator, called Ceres-Mithra, to predict spatial maps of radionuclide concentrations at different instants. This computer code depends on many uncertain scalar and temporal parameters, describing the radionuclide, release or weather characteristics. The purpose is to detect the input parameters the uncertainties of which highly affect the predicted concentrations and to quantify their influences. To this end, we present various measures for the sensitivity analysis of a spatial model. Some of them lead to as many analyses as spatial locations (site sensitivity indices) while others consider a single one, with respect to the whole spatial domain (block sensitivity indices). For both categories, variance-based and dependence measures are considered, based on recent literature. All of these sensitivity measures are applied to the C-M computer code and compared to each other, showing the complementarity of block and site sensitivity analyses. Finally, a sensitivity analysis summarizing the input uncertainty contribution over the entirety of the spatio-temporal domain is proposed.

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  1. For any pixel \(\mathbf {z}_i\in \mathcal {Z}\), the predictivity coefficient is defined by \(Q^2(\mathbf {z}_i)=1-\frac{\mathbb {E}\left[ \left( \hat{f}_i(\mathbf {X})-f_i(\mathbf {X})\right) ^2\right] }{\mathbb {V}\left[ f_i(\mathbf {X})\right] }\), where \(f_i(\mathbf {X})\) and \(\hat{f}_i(\mathbf {X})\) are the outputs values at pixel \(\mathbf {z}_i\) given by the numerical simulator \(\mathbf {f}\) and the predictor \(\hat{\mathbf {f}}\) respectively. \(Q^2(\mathcal {Z})\) gives us the whole map of explained output variance. \(Q^2\) corresponds to the coefficient of determination \(R^2\) in prediction.


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Correspondence to Matthias De Lozzo.


Appendix 1: R code for the HSIC function

figure a

Appendix 2: R code for the RDC function

figure b

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De Lozzo, M., Marrel, A. Sensitivity analysis with dependence and variance-based measures for spatio-temporal numerical simulators. Stoch Environ Res Risk Assess 31, 1437–1453 (2017).

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