Abstract
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.
Highlights
Sensitivity analysis is widely used for modelling studies in public health, since the number of parameters involved is often high
For the warped wavelet estimator, we propose a model selection procedure based on a work by Laurent and Massart [21] to make the estimator adaptive
Sensitivity analysis is a key step in modelling studies, in particular in epidemiology
Summary
Sensitivity analysis is widely used for modelling studies in public health, since the number of parameters involved is often high (see e.g. [31, 36] and references therein). Meta-models are used: approximating the mean and the dispersion of the response by deterministic functions allows to come back to the classical deterministic framework (e.g. Janon et al [18], Marrel et al [23]) We study here another point of view, which is based on the non-parametric statistical estimation of the term Var E[Y | X ] appearing in the numerator of (1.1). We propose here a new approach based on warped wavelet decompositions introduced by Kerkyacharian and Picard [20] An advantage of these non-parametric estimators is that their computation requires less simulations of the model. C denotes a constant that can vary from line to line
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