TY - JOUR
T1 - Verified propagation of imprecise probabilities in non-linear ODEs
AU - Gray, Ander
AU - Forets, Marcelo
AU - Schilling, Christian
AU - Ferson, Scott
AU - Benet, Luis
N1 - Publisher Copyright:
© 2023
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - Reachability analysis
KW - Dynamical systems
KW - Automatically verified
KW - Imprecise probabilities
KW - P-boxes
UR - http://www.scopus.com/inward/record.url?scp=85174824256&partnerID=8YFLogxK
U2 - 10.1016/j.ijar.2023.109044
DO - 10.1016/j.ijar.2023.109044
M3 - Journal article
AN - SCOPUS:85174824256
SN - 0888-613X
VL - 164
JO - International Journal of Approximate Reasoning
JF - International Journal of Approximate Reasoning
ER -