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

7.5 Sensitivity Analysis and Importance Ranking

Chapter 2 showed how important it is for most types of risk or uncertainty assessment to undertake sensitivity analysis (or importance ranking) as part of the process. Sensitivity analysis involves also uncertainty propagation but the output requires dedicated post-treatment as one not only looks for the risk measure itself, but also requires input-output quantities called sensitivity indices (or importance measures) that enable a deeper understanding of the input-output mapping. Sensitivity analysis is a vast field of applied science and will only be briefly introduced hereafter in close connection with the propagation methods and regularity issues reviewed earlier. The reader should refer to the specialised textbooks or literature, such as Saltelli et al., (2004).

7.5.1 Elementary Indices and Importance Measures and their Equivalence in Linear System Models

Before getting into numerical indices, the use of graphical methods is generally recommended as they give powerful insights through simple techniques. A simple approach to start with is to generate a sample (typically at random) and to use scatterplots visualising the results by couples for each i-th uncertain input. Even though very simple, such an approach enables the detection of more than linear or monotonous dependence although it is limited somewhat regarding the interactions ...