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Sensitivity analysis with dependent random variables : Estimation of the Shapley effects for unknown input distribution and linear Gaussian models

Abstract : Sensitivity analysis is a powerful tool to study mathematical models and computer codes. It reveals the most impacting input variables on the output variable, by assigning values to the the inputs, that we call "sensitivity indices". In this setting, the Shapley effects, recently defined by Owen, enable to handle dependent input variables. However, one can only estimate these indices in two particular cases: when the distribution of the input vector is known or when the inputs are Gaussian and when the model is linear. This thesis can be divided into two parts. First, the aim is to extend the estimation of the Shapley effects when only a sample of the inputs is available and their distribution is unknown. The second part focuses on the linear Gaussian framework. The high-dimensional problem is emphasized and solutions are suggested when there are independent groups of variables. Finally, it is shown how the values of the Shapley effects in the linear Gaussian framework can estimate of the Shapley effects in more general settings.
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Submitted on : Friday, October 23, 2020 - 3:18:12 PM
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Baptiste Broto. Sensitivity analysis with dependent random variables : Estimation of the Shapley effects for unknown input distribution and linear Gaussian models. Statistics [math.ST]. Université Paris-Saclay, 2020. English. ⟨NNT : 2020UPASS119⟩. ⟨tel-02976702⟩

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