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

7.3 Classical Alternatives to Direct Monte-Carlo sampling

7.3.1 Overview of the Computation Alternatives to MCS

When computational constraints prove to be substantially limiting, it is still possible to undertake alternatives to MCS. An abundant literature and a great deal of on-going research are devoted to that task, in particular concerning structural reliability. In other words, the methods aim at increasing the computational rarity index beyond the RI < −2 (standard MCS) or RI < −0.5 (Wilks). As will be discussed below, they should always be striking the best compromise between:

• Realistic computational time (i.e. a limited number of calls to G(.)). This depends, according to the method, on the number of variables (i.e. the dimension of X or Z) and/or the criterion c_z.
• Appropriate level of control of accuracy, i.e. of the propagation uncertainty. This is critically dependent on the criterion c_z under consideration and on the characteristics of the regularity of the deterministic model G(.) (e.g. linearity, monotonicity, limited variations etc.).

Table 7.9 provides a synoptic view of the methods that will be reviewed subsequently.The various alternatives to MCS are positioned within the compromise computational cost vs. accuracy control. Note particularly that this compromise depends essentially upon the risk measure that has been chosen for the study: some methods are specific to certain risk measures, such as the probability of exceeding a threshold and are generally highly ...