Sensitivity analysis for multidimensional and functional outputs

Abstract : Let $X:=(X_1, \ldots, X_p)$ be random objects (the inputs), defined on some probability space $(\Omega,{\mathcal{F}}, \mathbb P)$ and valued in some measurable space $E=E_1\times\ldots \times E_p$. Further, let $Y:=Y = f(X_1, \ldots, X_p)$ be the output. Here, $f$ is a measurable function from $E$ to some Hilbert space $\mathbb{H}$ ($\mathbb{H}$ could be either of finite or infinite dimension). In this work, we give a natural generalization of the Sobol indices (that are classically defined when $Y\in\R$ ), when the output belongs to $\mathbb{H}$. These indices have very nice properties. First, they are invariant. under isometry and scaling. Further they can be, as in dimension $1$, easily estimated by using the so-called Pick and Freeze method. We investigate the asymptotic behaviour of such estimation scheme.
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Contributeur : Alexandre Janon <>
Soumis le : jeudi 7 novembre 2013 - 15:08:54
Dernière modification le : mercredi 12 décembre 2018 - 15:22:59
Document(s) archivé(s) le : samedi 8 février 2014 - 09:35:13


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  • HAL Id : hal-00881112, version 1
  • ARXIV : 1311.1797


Fabrice Gamboa, Alexandre Janon, Thierry Klein, Agnès Lagnoux. Sensitivity analysis for multidimensional and functional outputs. 2013. 〈hal-00881112〉



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