Dependent Possibilistic Arithmetic Using Copulas

Gray, Ander ORCID: 0000-0002-1585-0900, Hose, Dominik, De Angelis, Marco ORCID: 0000-0001-8851-023X, Hanss, Michael and Ferson, Scott ORCID: 0000-0002-2613-0650
(2021) Dependent Possibilistic Arithmetic Using Copulas. In: International symposium on imprecise probability: theory and applications (ISPTA2021), 2021-7-6 - 2021-7-9, Granada, Spain.

[img] Text
gray21-2.pdf - Published version

Download (1MB) | Preview


We describe two functions on possibility distributions which allow one to compute binary operations with dependence either specified by a copula or partially defined by an imprecise copula. We use the fact that possibility distributions are consonant belief functions to aggregate two possibility distributions into a bivariate belief function using a version of Sklar’s theorem for minitive belief functions, i.e. necessity measures. The results generalise previously published independent and Fréchet methods, allowing for any stochastic dependence to be specified in the form of a (imprecise) copula. This new method produces tighter extensions than previous methods when a precise copula is used. These latest additions to possibilistic arithmetic give it the same capabilities as p-box arithmetic, and provides a basis for a p-box/possibility hybrid arithmetic. This combined arithmetic provides tighter bounds on the exact upper and lower probabilities than either method alone for the propagation of general belief functions.

Item Type: Conference or Workshop Item (Unspecified)
Uncontrolled Keywords: Possibility Theory, P-box, Copulas, Probabilistic Arithmetic, Probability Bounds Analysis, Imprecise Probabilities
Divisions: Faculty of Science and Engineering > School of Engineering
Depositing User: Symplectic Admin
Date Deposited: 18 Jun 2021 07:08
Last Modified: 22 Jul 2023 21:09
Related URLs: