Probability boxes as info-gap models

Abstract

Just as an interval bounds an uncertain real value, a probability box bounds an uncertain cumulative distribution function. It can express doubt about the shape of a probability distribution, the distribution parameters, the nature of intervariable dependence, or some other aspect of model uncertainty. Probability bounds analysis rigorously projects probability boxes through mathematical expressions. Ben-Haim's info-gap decision theory is a non-probabilistic decision theory that can address poorly characterized and even unbounded uncertainty. It bases decisions on optimizing robustness to failure rather than expected utility. Nested probability boxes can be used to define info-gap models for probability distributions, and probability bounds analysis provides a ready calculus for the calculations needed for an info-gap analysis involving probabilistic uncertainty.

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