Matthias Troffaes, Sebastien Destercke

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Probability boxes on totally preordered spaces for multivariate modelling

Abstract

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.

Keywords

p-box, natural extension, multivariate, elicitation, independence, Fréchet, lower prevision

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Authors’ addresses

Matthias Troffaes
Department of Mathematical Sciences
Durham University
Science Laboratories, South Road
Durham, DH1 3LE

Sebastien Destercke
UMR IATE, Campus INRA / Montpellier SupAgro 2, place Pierre Viala 34060 Montpellier Cedex 2

E-mail addresses

Matthias Troffaes		matthias.troffaes@gmail.com
Sebastien Destercke		sdestercke@gmail.com