Verified propagation of imprecise probabilities in non-linear ODEs

Gray, Ander ORCID: 0000-0002-1585-0900, Forets, Marcelo, Schilling, Christian, Ferson, Scott ORCID: 0000-0002-2613-0650 and Benet, Luis (2024) Verified propagation of imprecise probabilities in non-linear ODEs. International Journal of Approximate Reasoning, 164. p. 109044.

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Abstract

We combine reachability analysis and probability bounds analysis, which allow for imprecisely known random variables (multivariate intervals or p-boxes) to be specified as the initial states of a dynamical system. In combination, the methods allow for the temporal evolution of p-boxes to be rigorously computed, and they give interval probabilities for formal verification problems, also called failure probability calculations in reliability analysis. The methodology places no constraints on the input probability distribution or p-box and can handle dependencies generally in the form of copulas. We also provide a consonant approximation method for multivariate p-boxes, which allows for the prediction sets of dynamical systems to be efficiently computed. The presented methodology is rigorous and automatically verified, as both the dynamics and uncertainties are represented and solved with guaranteed enclosures.

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	19 Mar 2024 08:38
Last Modified:	19 Mar 2024 08:38
DOI:	10.1016/j.ijar.2023.109044
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3179663