A randomized orthogonal array-based procedure for the estimation of first- and second-order Sobol' indices
| Autor: | Clémentine Prieur, Jean-Yves Tissot |
|---|---|
| Přispěvatelé: | Mathematics and computing applied to oceanic and atmospheric flows (AIRSEA), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS), Inria Grenoble - Rhône-Alpes, Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Mathematical optimization Generalization Calibration (statistics) 010103 numerical & computational mathematics 01 natural sciences orthogonal arrays 010104 statistics & probability [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] variance-based sensitivity indices Applied mathematics 14. Life underwater Sensitivity (control systems) 0101 mathematics Mathematics Applied Mathematics Sobol sequence Variance (accounting) Numerical integration global sensitivity analysis Modeling and Simulation numerical integration Monte Carlo integration Statistics Probability and Uncertainty Orthogonal array [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | Journal of Statistical Computation and Simulation Journal of Statistical Computation and Simulation, Taylor & Francis, 2015, 85 (7), pp.1358-1381. ⟨10.1080/00949655.2014.971799⟩ Journal of Statistical Computation and Simulation, 2015, 85 (7), pp.1358-1381. ⟨10.1080/00949655.2014.971799⟩ |
| ISSN: | 1563-5163 0094-9655 |
| DOI: | 10.1080/00949655.2014.971799 |
| Popis: | International audience; In variance-based sensitivity analysis, the method of Sobol' (1993) allows to compute Sobol' indices using Monte Carlo integration. One of the main drawbacks of this approach is that the estimation of Sobol' indices requires the use of several samples. For example, in a d-dimensional space, the estimation of all the first-order Sobol' indices requires d+1 samples. Some interesting combinatorial results have been introduced to weaken this defect, in particular by Saltelli (2002) and more recently by Owen (2012) but the quantities they estimate still require O(d) samples. In this paper, we introduce a new approach to estimate for any k all the k-th order Sobol' indices by using only two samples. We establish theoretical properties of such a method for the first-order Sobol' indices and discuss the generalization to higher-order indices. As an illustration, we propose to apply this new approach to a marine ecosystem model of the Ligurian sea (northwestern Mediterranean) in order to study the relative importance of its several parameters. The calibration process of this kind of chemical simulators is well-known to be quite intricate, and a rigorous and robust --- i.e. valid without strong regularity assumptions --- sensitivity analysis, as the method of Sobol' provides, could be of great help. |
| Databáze: | OpenAIRE |
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