Estimation of Small Quantile Sets Using a Sequential Bayesian Strategy
Résumé
Given a numerical simulator of a physical phenomenon or system, one often seeks to determine the set of inputs that lead to values with specified properties. This type of problem, broadly known as "set inversion," has several variants, depending on the properties sought for the outputs.
In this communication, we concentrate on a specific robust set inversion problem termed “quantile set inversion" (QSI). In this context, the function of interest has both deterministic and uncertain inputs. The objective within this framework is to estimate the set of deterministic inputs so that the probability—with respect to the distribution of the uncertain inputs—of the output variables falling within a given range is below a given threshold.
To address this problem, we recently proposed (Ait Abdelmalek-Lomenech, Bect, Chabridon & Vazquez, arXiv:2211.01008v2, 2023) a sequential Bayesian sampling strategy based on the Stepwise Uncertainty Reduction (SUR) principle. We now suggest an adaptation of this method, employing sequential Monte Carlo (SMC) sampling, to tackle cases where the set to be estimated is small compared to the full domain of deterministic inputs.
Domaines
Statistiques [stat]
Origine : Fichiers produits par l'(les) auteur(s)