Échantillonnages Monte Carlo et quasi-Monte Carlo pour l'estimation des indices de Sobol'. Application à un modèle transport-urbanisme

Laurent Gilquin 1, 2
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : Land Use and Transportation Integrated (LUTI) models have become a norm for representing the interactions between land use and the transportation of goods and people in a territory. These models are mainly used to evaluate alternative planning scenarios, simulating their impact on land cover and travel demand. LUTI models and other mathematical models used in various fields are most of the time based on complex computer codes. These codes often involve poorly-known inputs whose uncertainties can have significant effects on the model outputs. Global sensitivity analysis methods are useful tools to study the influence of the model inputs on its outputs. Among the large number of available approaches, the variance based method introduced by Sobol' allows to calculate sensitivity indices called Sobol' indices. These indices quantify the influence of each model input on the outputs and can detect existing interactions between inputs. In this framework, we favor a particular method based on replicated designs of experiments called replication method. This method appears to be the most suitable for our application and is advantageous as it requires a relatively small number of model evaluations to estimate first-order or second-order Sobol' indices. This thesis focuses on extensions of the replication method to face constraints arising in our application on the LUTI model Tranus, such as the presence of dependency among the model inputs, as far as multivariate outputs. Aside from that, we propose recursive approaches to sequentially estimate Sobol' indices. With these approaches, more accurate Sobol' estimates are obtained while recycling previous sets of model evaluations. One of these approaches corresponds to a recursive version of the replication method and is based on the iterative construction of stratified designs, latin hypercubes and orthogonal arrays. A second approach combines the use of quasi-Monte Carlo sampling and the construction of a new stopping criterion. An application of our contributions on the LUTI model Tranus is presented.
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Laurent Gilquin. Échantillonnages Monte Carlo et quasi-Monte Carlo pour l'estimation des indices de Sobol'. Application à un modèle transport-urbanisme. Statistiques [math.ST]. Université Grenoble Alpes, 2016. Français. ⟨tel-01403914v1⟩

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