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

5 A Reading Guide Through the Chapters

The concepts and formulations in this book have an essential grounding in practice throughout the variety of domains which are reviewed in Chapter 1: natural risk, industrial risk and process optimisation, metrology, environmental and sanitary protection, and engineering economics. Common key steps and considerable mathematical synergies will be generated within a generic modelling framework described in Chapter 2. Chapter 4 discusses the practical implementation of the various risk/uncertainty measures or criteria that all come into the generic framework, but correspond to different epistemological options coming from decision-theory. This relates in particular to the classical concern of distinguishing according to the aleatory or epistemic nature of uncertainty, specifying more clearly the variability to be covered by the risk measure, mixing deterministic and probabilistic settings, or specifying temporal conventions with the building of composite risk measures (confidence intervals on top of exceedance probabilities, peak events in time, etc.).

Hence, a number of statistical and computing challenges stand as generic to a number of situations. Estimation issues with samples and expertise are discussed in two chapters. Firstly, in Chapter 5 with the case where direct information is available on the uncertain variables or risk components. Simultaneous estimation of both aleatory and epistemic components involves classical or Bayesian statistics ...