Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

2.2 Decisional Quantities and Goals of Modelling Under Risk and Uncertainty

2.2.1 The Key Concept of Risk Measure or Quantity of Interest

The consideration of risk and uncertainty with regard to the system means of course that there is no intention to control the exact value of z at the time of interest, conditional on actions d. Knowledge of the system may encompass a variety of past observations of some features of the system, phenomenological or logical arguments supporting the prediction of certain limits or regularities on the states of the system, all more or less directly connected to the variables or events of interest z. Nonetheless, by the above definition, there will always be knowledge limitations within the state of the system. The best that may be hoped for is to infer possible or likely ranges for z.

Many frameworks could be potentially mobilised in order to represent such uncertain values or ranges, such as probability theory, deterministic interval computation, possibility theory, fuzzy logic or the Dempster-Shafer or Evidence Theory that may be seen as theoretically encompassing all of the former. While the literature has discussed to a large extent the pros and cons of various probabilistic or non-probabilistic paradigms (see, e.g. Helton and Oberkampf,), this book is centred on the use of the probabilistic framework which has a number of desirable decision-making properties, as will be briefly recalled in Chapter 4. Besides, the review in Chapter 1 has shown ...