Fisher-Rao distance between truncated distributions and robustness analysis in uncertainty quantification - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Fisher-Rao distance between truncated distributions and robustness analysis in uncertainty quantification

Résumé

Input variables in numerical models are often subject to several levels of uncertainty, usually modeled by probability distributions. In the context of uncertainty quantification applied to these models, studying the robustness of output quantities with respect to the input distributions requires: (a) defining variational classes for these distributions; (b) calculating boundary values for the output quantities of interest with respect to these variational classes. The latter should be defined in a way that is consistent with the information structure defined by the “baseline” choice of input distributions. Considering parametric families, the variational classes are defined using the geodesic distance in their Riemannian manifold, a generic approach to such problems. Theoretical results and application tools are provided to justify and facilitate the implementation of such robustness studies, in concrete situations where these distributions are truncated -- a setting frequently encountered in applications. The feasibility of our approach is illustrated in a simplified industrial case study.
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Dates et versions

hal-04660215 , version 1 (30-07-2024)

Identifiants

Citer

Baalu Belay Ketema, Nicolas Bousquet, Francesco Costantino, Fabrice Gamboa, Bertrand Iooss, et al.. Fisher-Rao distance between truncated distributions and robustness analysis in uncertainty quantification. 2024. ⟨hal-04660215⟩
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