Copulas, lower probabilities and random sets: how and when to apply them?

Roman Malinowski (1, 2) , Sébastien Destercke (2)

1 CNES - Centre National d'Études Spatiales [Toulouse]
2 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

A copula is an aggregation function, that can be used as a dependency model. Any multivariate distribution function can be characterized by its marginals and a copula. When introducing imprecision in the modelling of those distribution functions, different solutions are available to aggregate the univariate uncertainty representations into a multivariate one via the copula. We present some of those solutions, and discuss their respective inclusions for special cases: independence, belief functions, necessity functions and p-boxes.

Domaines: Informatique [cs]

Roman Malinowski, Sébastien Destercke. Copulas, lower probabilities and random sets: how and when to apply them?. 10th International Conference on Soft Methods in Probability and Statistics (SMPS 2022), Sep 2022, Valladolid, Spain. pp.271-278, ⟨10.1007/978-3-031-15509-3_36⟩. ⟨hal-03794204⟩