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

Abstract

In many practical situations, we only know the upper bound Δ on the (absolute value of the) measurement error Δx that is, we only know that the measurement error is located on the interval [-Δ,Δ]. The traditional engineering approach to such situations is to assume that Δx is uniformly distributed on [-Δ,Δ], and to use the corresponding statistical techniques. 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 chapter, we provide a brief overview of related algorithms, results, and remaining open problems.