Towards Integration of Probabilistic and Interval Errors in Engineering Calculations

In many engineering applications, we have to combine probabilistic and interval errors. 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 know the values with interval uncertainty. For example, if we did not detect any pollution, the pollution value can be anywhere between 0 and the detection limit DL. Another example: to study the effect of a pollutant on the fish, we check on the fish daily; if a fish was alive on Day 5 but dead on Day 6, then the lifetime of this fish is ∈ [5, 6]. We must modify the existing statistical algorithms to process such interval data. In general, the resulting problems are NP-hard [1,2]. In this talk, we survey cases when feasible algorithms exist: e.g., when measurements are very accurate, or when all the measurements are done with one (or few) instruments