On the connection between probability boxes and possibility measures

Troffaes, Matthias C.M.; Miranda, Enrique; Destercke, Sebastien

doi:10.1016/j.ins.2012.09.033

On the connection between probability boxes and possibility measures

Troffaes, Matthias C.M.; Miranda, Enrique; Destercke, Sebastien

Authors

Professor Matthias Troffaes matthias.troffaes@durham.ac.uk
Professor

Enrique Miranda

Sebastien Destercke

Abstract

We explore the relationship between possibility measures (supremum preserving normed measures) and p-boxes (pairs of cumulative distribution functions) on totally preordered spaces, extending earlier work in this direction by De Cooman and Aeyels, among others. We start by demonstrating that only those p-boxes who have 0-1-valued lower or upper cumulative distribution function can be possibility measures, and we derive expressions for their natural extension in this case. Next, we establish necessary and sufficient conditions for a p-box to be a possibility measure. Finally, we show that almost every possibility measure can be modelled by a p-box, simply by ordering elements by increasing possibility. Whence, any techniques for p-boxes can be readily applied to possibility measures. We demonstrate this by deriving joint possibility measures from marginals, under varying assumptions of independence, using a technique known for p-boxes. Doing so, we arrive at a new rule of combination for possibility measures, for the independent case.

Citation

Troffaes, M. C., Miranda, E., & Destercke, S. (2013). On the connection between probability boxes and possibility measures. Information Sciences, 224, 88-108. https://doi.org/10.1016/j.ins.2012.09.033

Journal Article Type	Article
Publication Date	Mar 1, 2013
Deposit Date	Nov 17, 2011
Publicly Available Date	Oct 17, 2014
Journal	Information Sciences
Print ISSN	0020-0255
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	224
Pages	88-108
DOI	https://doi.org/10.1016/j.ins.2012.09.033
Keywords	Probability boxes, Possibility measures, Maxitive measures, Coherent lower and upper probabilities, Natural extension.
Publisher URL	http://dx.doi.org/10.1016/j.ins.2012.09.033
Related Public URLs	http://arxiv.org/abs/1103.5594

Files

Accepted Journal Article (258 Kb)
PDF

Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Information sciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Information sciences, 224, 2014, 10.1016/j.ins.2012.09.033.