Nonparametric adaptive estimation of order 1 Sobol indices in stochastic models, with an application to Epidemiology
Résumé
The global sensitivity analysis is a set of methods aiming at quantifying the influence of the uncertainty about the inputs parameters of a model on the variability of the responses. In a deterministic framework, i.e. when the same inputs values give always the same outputs values, the estimation of the Sobol indices is a commonly-used method. This method is based on the variance decomposition aiming at estimating the contribution of each parameter (or combination of parameters) on the variance of the response. We consider here the estimation of the Sobol indices of order 1, which are usually estimated by replicated simulations of the model. In the case of a stochastic framework, i.e. when the model response is not unique for a same input parameter set due to random numbers generation in the model, metamodels are often used to approximate the mean and the dispersion of the response by deterministic functions thus allowing to recover the classical deterministic framework. 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 it is adaptative 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.
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