The one hundredth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, May 28, 2026.
2–3 PM — Julien Bect & Xujia Zhu ( L2S, CentraleSupélec)
(Goal-Oriented) Global Sensitivity Analysis Revisited:The Mystery of the Camembert Slices
Sensitivity analysis plays a critical role in uncertainty quantification, aiming to characterize how uncertainty in model inputs propagates through computational models or experiments to the outputs. In contrast to local approaches, global methods account for variability over the entire input space, providing a more thorough description of input-output relationships. A wide range of global sensitivity indices has been proposed over the past decades, particularly to define so-called closed sensitivity indices , which quantify the joint contribution of a group (or coalition) of input variables.
From closed indices, one can easily derive first-order (main) effects and higher-order interaction effects. A desirable property in this setting is the non-negativity of the resulting sensitivity indices, which yields an interpretable decomposition of the total uncertainty, much like a pie chart---or ``Camembert'' diagram, as it is sometimes called in French---partitions a whole into non-overlapping contributions. However, this property does not hold in general. In fact, beyond the well-known case of variance-based (Sobol') sensitivity indices, to the best of our knowledge, only two frameworks ensure non-negative higher-order indices, both of them discovered quite recently by Da Veiga [1]: the first one relies on the expected Maximum Mean Discrepancy (MMD) between the conditional and the marginal distribution, while the second one leverages the Hilbert--Schmidt Independence Criterion (HSIC) in combination with specific (ANOVA) kernels.
In this talk, we first review three constructions of closed sensitivity indices available in the literature, in relation with the key notion of uncertainty functional [2]. Then we present a unified framework [3] that clarifies the common mechanism at work in the two classes of indices proposed by Da Veiga. At the heart of this framework resides a new avatar of the Sobol'-Hoeffding decomposition, also known as the functional ANOVA decomposition. Finally, we discuss several open questions and directions for future research, in particular regarding general necessary and sufficient conditions for higher-order indices to be non-negative.
References:
- [1] Kernel-based ANOVA decomposition and Shapley effects—application to global sensitivity analysis, 2021
- [2] Uncertainty functionals revisited: Concavity and Jensen’s inequality, 2026
- [3] On non-negative coalitioal decompositions in global sensitivity analysis, in preparation, 2026
Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).
Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)
Practical details: the seminar will be held online using Microsoft Teams.
If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).
You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.
The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.
