Dependent possibilistic arithmetic using copulas

Ander Gray, Dominik Hose, Marco de Angelis, Michael Hanss, Scott Ferson

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

5 Citations (Scopus)

Abstract

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.
Original languageEnglish
Title of host publicationThe 19th IEEE International Symposium on Parallel and Distributed Processing with Applications (IEEE ISPA 2021)
Place of PublicationPiscataway, N.J.
PublisherIEEE
Pages169-179
Number of pages11
ISBN (Print)9780738126463
Publication statusPublished - 3 Oct 2021
EventThe 19th IEEE International Symposium on Parallel and Distributed Processing with Applications (IEEE ISPA 2021) - New York, United States
Duration: 30 Sept 20213 Oct 2021

Conference

ConferenceThe 19th IEEE International Symposium on Parallel and Distributed Processing with Applications (IEEE ISPA 2021)
Abbreviated titleISPTA 2021
Country/TerritoryUnited States
CityNew York
Period30/09/213/10/21

Keywords

  • possibility theory
  • P-box
  • copulas
  • probabilistic arithmetic
  • probability bounds analysis
  • imprecise probabilities

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