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

2.7 Summary: Main Steps of the Studies and Later Issues

Quantitative risk and uncertainty studies involve the prediction of the key characteristics of a system (vector Z of variables/events of interest) at a given time, the state of which depends on actions (vector d) taken in an imperfectly known manner. Whatever the diversity of the contexts reviewed in Chapter 1, two closely-associated models are mobilised:

• the system model M_s(x, d, u) and associated observational and predictive formulations,
• the uncertainty model in its input variables, events, parameters and residuals.

Together they help estimate the appropriate risk measure (or quantity of interest): a risk measure c_z(d) is a functional that summarises the level of risk/uncertainty affecting Z conditioned by the given actions in the system. It plays a central role in fulfilling any of the four salient goals of studying the system under uncertainty: understanding the behaviour of the system; accrediting or validating a model; selecting or optimising a set of actions; and complying with a given decision-making criterion or regulatory target.

Phenomenological knowledge and statistical or non-statistical information are all necessary to estimate the two associated models in a joint effort to best represent the information available. Selecting the adequate risk measure requires a definition of the uncertainty setting that mixes ...