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A tradeoff between explorations and repetitions for estimators of two global sensitivity indices in stochastic models induced by probability measures

Abstract : Sobol sensitivity indices assess how the output of a given mathematical model is sensitive to its inputs. If the model is stochastic then it cannot be represented as a function of the inputs, thus raising questions as how to do a sensitivity analysis in those models. Practitioners have been using a method that exploits the availability of softwares for deterministic models. For each input, the stochastic model is repeated and the outputs are averaged. These averages are seen as if they came from a deterministic model and hence Sobol's method can be used. However, in the context of limited computational resources, one must ensure that the number of repetitions of the stochastic model multiplied by the number of explorations of the input space is less than a fixed threshold. The problem of finding an optimal tradeoff between the repetitions and the explorations is addressed. A bound on an error criterion that penalizes bad rankings of the inputs' sensitivities is minimized. The estimator induced by the empirical method described above is shown to be asymptotically biased if the number of repetitions goes to infinity too slowly. A functional relationship between the output, the input and some random noise is derived from minimal distributional assumptions, which leads to a new sensitivity index with better statistical properties. The theory is illustrated on numerical experiments.
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https://hal.archives-ouvertes.fr/hal-02113448
Contributor : Gildas Mazo <>
Submitted on : Friday, May 7, 2021 - 9:18:05 AM
Last modification on : Saturday, June 5, 2021 - 3:42:15 AM

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  • HAL Id : hal-02113448, version 5

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Gildas Mazo. A tradeoff between explorations and repetitions for estimators of two global sensitivity indices in stochastic models induced by probability measures. 2021. ⟨hal-02113448v5⟩

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