Probability boxes on totally preordered spaces for multivariate modelling

Troffaes M.C.M Matthias (1) , Sébastien Destercke (2)

1 Department of Mathematical Sciences
2 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

Probability boxes (pairs of cumulative distribution functions) are among the most popular models used in imprecise probability theory. In this paper, we provide new efficient tools to construct multivariate p-boxes and develop algorithms to draw inferences from them. For this purpose, we formalise and extend the theory of p-boxes using lower previsions. We allow p-boxes to be defined on arbitrary totally preordered spaces, hence thereby also admitting multivariate p-boxes. We discuss the construction of multivariate p-boxes under various independence assumptions. An example demonstrates the practical feasibility of our results.

Mots clés: p-box; natural extension; multivariate; elicitation; independence; Fréchet; lower prevision

Domaines: Probabilités [math.PR]; Applications [stat.AP]

Troffaes M.C.M Matthias, Sébastien Destercke. Probability boxes on totally preordered spaces for multivariate modelling. Seventh International Symposium on Imprecise Probability: Theories and Applications (ISIPTA), Jul 2011, Innsbruck, Austria. pp.343-353. ⟨hal-00655598⟩