Verified bounds on the imprecise failure probability with the SIVIA algorithm

De Angelis, Marco and Gray, Ander (2023) Verified bounds on the imprecise failure probability with the SIVIA algorithm. In: 13th International Symposium on Imprecise Probabilities: Theories and Applications, 2023-07-11 - 2023-07-14, Universidad de Oviedo.

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Abstract

In this work, we explore the use of SIVIA (Set Inversion Via Interval Analysis) on failure probability problems formulated with imprecision. Because of the imprecision the integration over the rigorous sub-paving can no longer be done only using the antiderivative of the joint or copula density, a.k.a. h-volume, because of sub-additivity. Under random-set independence, or precise copulas and on small problems (≤ variables), the imprecise failure probability can be obtained counting the intersections with the sub-pavings of all focal elements in the space product. The joint focal elements that are fully contained in the failure sub-paving correspond to the belief---failure probability lower bound. On larger problems, the space product is no longer possible; we replace it by random slicing. The approximation introduced by the random slicing is controlled by a given level of confidence, which typically decreases the more slices are evaluated.

ORCID iDs

De Angelis, Marco ORCID logoORCID: https://orcid.org/0000-0001-8851-023X and Gray, Ander;
CORE (COnnecting REpositories)