Towards combining probabilistic and interval uncertainty in engineering calculations: Algorithms for computing statistics under interval uncertainty, and their computational complexity

In many engineering applications, we have to combine probabilistic and interval uncertainty. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In environmental measurements, we often only measure the values with interval uncertainty. We must therefore modify the existing statistical algorithms to process such interval data. In this paper, we provide a survey of algorithms for computing various statistics under interval uncertainty and their computational complexity. The survey includes both known and new algorithms.