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

4.1 Natures of Uncertainty: Theoretical Debates and Practical Implementation

4.1.1 Defining Uncertainty – Ambiguity about the Reference

Uncertainty is such a pervasive concept that any attempt to give a clear-cut and complete definition may be presumptuous. Indeed, the subject spans a wide range of scientific and practical knowledge. From the narrower quantitative perspective of the book, Chapter 2 delineated that uncertainty is viewed as the extent of imperfect knowledge of the state (x, z) of a system conditional on taking given actions (d) at a given time (or period of time). It is quantified mathematically through the risk measure or quantity of interest over the possible or likely values of the output(s) of interest.

In essence, modelling under uncertainty will try to predict likely deviations from a predicted state or likely subsets of the space of possible states. A tempting interpretation of such a broad definition could be: ‘when the appropriate time (or period of time) comes up, the true realisation of the state of the system should fall within the extent predicted by the risk measure’. Note that such a definition presupposes implicitly the existence and observability of a true value for the state of the system. This is why a first condition, when undertaking uncertainty assessment, is to specify the system and output of interest considered carefully so as to avoid confusing it with ambiguity.

However, this is problematic to some extent. On the one hand, the specification ...