Introduction and Necessary Distinctions

At the beginning of the previous century, it was traditional among engineers and physicists to perform an error analysis of both measurements and computations (Dubbel 1939). The enormous computational capabilities, that became available since, enabled the development of complex computer models. They make use of numerous parameters, various sub-models and large numbers of input data subject to uncertainty that is, however, frequently ignored. One of the reasons in the past was the difficulty, if not impossibility, of performing an uncertainty analysis of the results from computationally demanding models. Combining powerful statistical methods, as described in the following chapters, with today’s computational capabilities opens the door to uncertainty analysis as a standard procedure. This chapter leads through the developmental stages of a computer model and points out their sources of epistemic uncertainties. The difference between “epistemic uncertainty” and “aleatoric uncertainty” is explained. It necessitates the use of two different interpretations of “probability” for their quantification. Epistemic uncertainty is quantified using subjective probability. The need for separation of epistemic and aleatoric uncertainties arises from the type of assessment question that is to be answered by the model result. This is explained and illustrated by practical examples.