The global sensitivity analysis is a set of methods aiming at quantifying thecontribution of an uncertain input parameter of the model (or combination ofparameters) on the variability of the response. We consider here the estimationof the Sobol indices of order 1 which are commonly-used indicators based on adecomposition of the output's variance. In a deterministic framework, when thesame inputs always give the same outputs, these indices are usually estimatedby replicated simulations of the model. In a stochastic framework, when theresponse given a set of input parameters is not unique due to randomness in themodel, metamodels are often used to approximate the mean and dispersion of theresponse by deterministic functions. We propose a new non-parametric estimatorwithout the need of defining a metamodel to estimate the Sobol indices of order1. The estimator is based on warped wavelets and is adaptive in the regularityof the model. The convergence of the mean square error to zero, when the numberof simulations of the model tend to infinity, is computed and an elbow effectis shown, depending on the regularity of the model.
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