Interval computations and interval-related statistical techniques: estimating uncertainty of the results of data processing and indirect measurements

In many practical situations, we only know the upper bound ∆ on the measurement error: |∆x| ≤ ∆. In other words, we only know that the measurement error is located on the interval [−∆,∆]. The traditional approach is to assume that ∆x is uniformly distributed on [−∆,∆]. In some situations, however, this approach underestimates the error of indirect measurements. It is therefore desirable to directly process this interval uncertainty. Such “interval computations” methods have been developed since the 1950s. In this paper, we provide a brief overview of related algorithms and results.