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| HAL: hal-00430171, version 4 |
| arXiv: 0911.1189 |
| Detailed view |  Export this paper |
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| Environmetrics 22 (2011) 383-397 |
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| Available versions: | v1 (2009-11-06) | v2 (2010-02-22) | v3 (2010-07-06) | v4 (2010-09-23) |
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| Global sensitivity analysis for models with spatially dependent outputs |
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Amandine Marrel 1Bertrand Iooss 2, 3 |
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| (2011) |
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| The global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol' indices. Metamodel-based techniques have been developed in order to replace the cpu time-expensive computer code with an inexpensive mathematical function, which predicts the computer code output. The common metamodel-based sensitivity analysis methods are well-suited for computer codes with scalar outputs. However, in the environmental domain, as in many areas of application, the numerical model outputs are often spatial maps, which may also vary with time. In this paper, we introduce an innovative method to obtain a spatial map of Sobol' indices with a minimal number of numerical model computations. It is based upon the functional decomposition of the spatial output onto a wavelet basis and the metamodeling of the wavelet coefficients by the Gaussian process. An analytical example is presented to clarify the various steps of our methodology. This technique is then applied to a real hydrogeological case: for each model input variable, a spatial map of Sobol' indices is thus obtained. |
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| 1: | IFP Energies Nouvelles (IFPEN) |
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IFP Energies Nouvelles |
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| 2: | GdR MASCOT-NUM ((Méthodes d'Analyse Stochastique des Codes et Traitements Numériques)) |
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CNRS : GDR3179 |
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| 3: | EDF R&D |
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EDF |
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| 4: | Laboratoire de Modélisation des Transferts dans l'Environnement |
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CEA |
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| 5: | Institut de Mathématiques de Toulouse (IMT) |
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Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219 |
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| 6: | Institute of Nuclear Reactors |
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RRC Kurchatov Institute |
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| Subject | : | Mathematics/Statistics Statistics/Statistics Theory |
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| Computer experiment – Gaussian process – metamodel – functional data – radionuclide migration |
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| hal-00430171, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00430171 | |
| oai:hal.archives-ouvertes.fr:hal-00430171 | |
| From: Bertrand Iooss | |
| Submitted on: Wednesday, 22 September 2010 08:09:41 | |
| Updated on: Thursday, 21 April 2011 19:14:28 | |
