Sensitivity analysis for multidimensional and functional outputs

By Fabrice Gamboa, Alexandre Janon, Thierry Klein, Agnès Lagnoux. 2013

133 citations recorded by the source corpus.

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 $Y\in\mathbb R$ ), 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.

Subfields: Mechanics of Materials, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dc3ed7525dd9bdcecf8636c5457ca8e3ab51a4df

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In Numerical Analysis

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Citations in the corpus

Global Sensitivity Analysis: a new generation of mighty estimators based on rank statistics (2020, background): “In particular, in [12], the authors recover the indices from [23] and show that they are a proper generalization of the classical Sobol indices in higher dimension.”