Probability boxes

Probability boxes

A probability box, also known as a p-box, is a mathematical construct used in the theory of imprecise probabilities. It is defined by a pair of cumulative distribution functions (CDFs) that form the upper and lower bounds of a probability family. The p-box represents an imprecisely known probability distribution, where the exact value is unknown but is within the range of the two bounding CDFs. It combines traditional probability theory with interval analysis and is a computationally practical calculation.From: Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures [2014], Residential flood risk in Metro Vancouver due to climate change using probability boxes [2023], Safety, Reliability and Risk Analysis: Beyond the Horizon [2013]

Discussion on evaluation of probability bounds applied to the Eurocode 7

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Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018

Sónia H. Marques

The optimisation-based probability box structure is constructed comparatively to the mean empirical cumulative distribution function, noted that the adjacent empirical functions corresponding to the collection of minimum and maximum values are sketched at a central credibility level 5σ. From observation of Figure 3 and Figure 5 it is noted that the position of the lowest minimum occurs on the inner part of the interval [0.1,1.0] for parameter a, with the position of the highest maximum on the coordinate 1.0. From observation of Figure 4 and Figure 6 it is noted that the gradual convergence of the major probability lines occurs whenever the correlation coefficient increases, with exception to the zone near the zero probability level on the minimum branch of the optimisation-based probability box structure at 0.9 correlation coefficient. This particular feature is observable because the lowest minimum occurs in the inner part of the interval [0.1,1.0] for parameter a.

Residential flood risk in Metro Vancouver due to climate change using probability boxes

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Journal Information

Published in International Journal of River Basin Management, 2023

Hiva Viseh, David N. Bristow

A probability box or a p-box is a computationally practical calculation of the theory of imprecise probabilities (Walley, 1991) which combines standard interval analysis with traditional probability theory (Beer et al., 2013; Ferson & Tucker, 2008).

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Discussion on evaluation of probability bounds applied to the Eurocode 7

Residential flood risk in Metro Vancouver due to climate change using probability boxes