Non-parametric adaptive estimation of order 1 Sobol indices in stochastic models, with an application to Epidemiology
| Autor: | Tran, Viet Chi, Castellan, Gwenaëlle, Cousien, Anthony, Tran, Chi |
|---|---|
| Přispěvatelé: | Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Infection, Anti-microbiens, Modélisation, Evolution (IAME (UMR_S_1137 / U1137)), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris 13 (UP13)-Université Paris Diderot - Paris 7 (UPD7)-Université Sorbonne Paris Cité (USPC), ANRS 95146, Chaire 'Modélisation Mathématique et Biodiversité' of Veolia Environnement-Ecole Polytechnique-Museum National d'Histoire Naturelle-Fondation X, ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), ANR-16-CE32-0007,CADENCE,Propagation de processus épidémiques sur des réseaux dynamiques de mouvements d’animaux avec application aux bovins en France(2016), Laboratoire Paul Painlevé (LPP), Université Paris 13 (UP13)-Université Paris Diderot - Paris 7 (UPD7)-Université Sorbonne Paris Cité (USPC)-Institut National de la Santé et de la Recherche Médicale (INSERM), ANR-16-CE32-0007,CADENCE,Propagation de processus épidémiques sur des réseaux dynamiques de mouvements d'animaux avec application aux bovins en France(2016), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Centre National de la Recherche Scientifique (CNRS)-Université de Lille |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences model selection Sensitivity analysis in a stochastic framework 49Q12 Mean squared error Stochastic modelling Mathematics - Statistics Theory Statistics Theory (math.ST) 62G08 62P10 applications to Epidemiology Statistics - Applications 01 natural sciences Nadaraya-Watson estimator 010104 statistics & probability [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] Convergence (routing) FOS: Mathematics Applied mathematics Applications (stat.AP) 0101 mathematics Randomness Mathematics [STAT.AP]Statistics [stat]/Applications [stat.AP] spread of the Hepatitis Virus C among drug users Model selection 010102 general mathematics adaptive non-parametric inference warped wavelets Nonparametric statistics Sobol indices of order 1 Estimator Sobol sequence [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie Statistics Probability and Uncertainty SIR model |
| Zdroj: | Electron. J. Statist. 14, no. 1 (2020), 50-81 Electronic journal of statistics Electronic journal of statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2020, 14 (1), pp.50-81. ⟨10.1214/19-EJS1627⟩ Electronic Journal of Statistics Electronic Journal of Statistics, 2020, 14 (1), pp.50-81. ⟨10.1214/19-EJS1627⟩ Electronic Journal of Statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2020, 14 (1), pp.50-81. ⟨10.1214/19-EJS1627⟩ |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/19-EJS1627⟩ |
| Popis: | International audience; Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the Sobol indices of order 1 which are commonly-used indicators based on a decomposition of the output's variance. In a deterministic framework, when the same inputs always give the same outputs, these indices are usually estimated by replicated simulations of the model. In a stochastic framework, when the response given a set of input parameters is not unique due to randomness in the model, metamodels are often used to approximate the mean and dispersion of the response by deterministic functions. We propose a new non-parametric estimator without the need of defining a metamodel to estimate the Sobol indices of order 1. The estimator is based on warped wavelets and is adaptive in the regularity of the model. The convergence of the mean square error to zero, when the number of simulations of the model tend to infinity, is computed and an elbow effect is shown, depending on the regularity of the model. Applications in Epidemiology are carried to illustrate the use of non-parametric estimators. |
| Databáze: | OpenAIRE |
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