This papers makes a brief review, in a relatively complete methodological framework, of various global sensitivity analysis methods of model output. Numerous statistical and probabilistic tools (regression, smoothing, tests, statistical learning, Monte Carlo, ...) aim at determining the model input variables which mostly contribute to an interest quantity depending of model output (as the variance of an output variable). Three kinds of methods are distinguished: the screening (coarse sorting of the most influential inputs among a large number), the measures of importance (quantitative sensitivity indices) and the deep exploration of the model behaviour (measuring the effects of inputs on their all variation range). A progressive application methodology is illustrated on a scholar application. A synthesis is given to place every method according to three axes: cost in number of model evaluations, model complexity and nature of brought information.
Cet article a pour objectif d’effectuer un survol rapide, mais dans un cadre méthodologique relativement complet, des différentes méthodes d’analyse de sensibilité globale d’un modèle numérique. Faisant appel à de nombreux outils statistiques (régression, lissage, tests, apprentissage, techniques de Monte Carlo, ...), celles-ci permettent de déterminer quelles sont les variables d’entrée d’un modèle qui contribuent le plus à une quantité d’intérêt calculée à l’aide de ce modèle (par exemple la variance d’une variable de sortie). Trois grandes classes de méthodes sont ainsi distinguées : le criblage (tri grossier des entrées les plus influentes parmi un grand nombre), les mesures d’importance (indices quantitatifs donnant l’influence de chaque entrée) et les outils d’exploration du modèle (mesurant les effets des entrées sur tout leur domaine de variation). Une méthodologie progressive d’application de ces techniques est illustrée sur une application à vocation pédagogique. Une synthèse est alors formulée afin de situer chaque méthode selon trois axes : coût en nombre d’évaluations du modèle, complexité du modèle et type d’information apportée.
Keywords: Computer code, Numerical experiment, Uncertainty, Metamodel, Design of experiments
@article{JSFS_2011__152_1_3_0, author = {Iooss, Bertrand}, title = {Revue sur l{\textquoteright}analyse de sensibilit\'e globale de mod\`eles num\'eriques}, journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique}, pages = {3--25}, publisher = {Soci\'et\'e fran\c{c}aise de statistique}, volume = {152}, number = {1}, year = {2011}, mrnumber = {2807168}, zbl = {1316.65016}, language = {fr}, url = {http://archive.numdam.org/item/JSFS_2011__152_1_3_0/} }
TY - JOUR AU - Iooss, Bertrand TI - Revue sur l’analyse de sensibilité globale de modèles numériques JO - Journal de la société française de statistique PY - 2011 SP - 3 EP - 25 VL - 152 IS - 1 PB - Société française de statistique UR - http://archive.numdam.org/item/JSFS_2011__152_1_3_0/ LA - fr ID - JSFS_2011__152_1_3_0 ER -
%0 Journal Article %A Iooss, Bertrand %T Revue sur l’analyse de sensibilité globale de modèles numériques %J Journal de la société française de statistique %D 2011 %P 3-25 %V 152 %N 1 %I Société française de statistique %U http://archive.numdam.org/item/JSFS_2011__152_1_3_0/ %G fr %F JSFS_2011__152_1_3_0
Iooss, Bertrand. Revue sur l’analyse de sensibilité globale de modèles numériques. Journal de la société française de statistique, Volume 152 (2011) no. 1, pp. 3-25. http://archive.numdam.org/item/JSFS_2011__152_1_3_0/
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