Publication details for Matthias TroffaesTroffaes, Matthias C. M., Miranda, Enrique & Destercke, Sebastien (2013). On the connection between probability boxes and possibility measures. Information Sciences 224: 88-108.
- Publication type: Journal Article
- ISSN/ISBN: 0020-0255
- DOI: 10.1016/j.ins.2012.09.033
- Keywords: Probability boxes, Possibility measures, Maxitive measures, Coherent lower and upper probabilities, Natural extension.
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Author(s) from Durham
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.