Mathematics – Probability
Scientific paper
2011-03-09
Mathematics
Probability
33 pages, 8 figures; v2: added keywords, added doi link
Scientific paper
10.1016/j.ijar.2011.02.001
A pair of lower and upper cumulative distribution functions, also called probability box or p-box, is among the most popular models used in imprecise probability theory. They arise naturally in expert elicitation, for instance in cases where bounds are specified on the quantiles of a random variable, or when quantiles are specified only at a finite number of points. Many practical and formal results concerning p-boxes already exist in the literature. 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 Walley's behavioural theory of imprecise probabilities, and heavily rely on its notion of natural extension and existing results about independence modeling. In particular, we allow p-boxes to be defined on arbitrary totally preordered spaces, hence thereby also admitting multivariate p-boxes via probability bounds over any collection of nested sets. We focus on the cases of independence (using the factorization property), and of unknown dependence (using the Fr\'echet bounds), and we show that our approach extends the probabilistic arithmetic of Williamson and Downs. Two design problems---a damped oscillator, and a river dike---demonstrate the practical feasibility of our results.
Destercke Sebastien
Troffaes Matthias C. M.
No associations
LandOfFree
Probability boxes on totally preordered spaces for multivariate modelling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Probability boxes on totally preordered spaces for multivariate modelling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Probability boxes on totally preordered spaces for multivariate modelling will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-644683