Sensitivity in risk analyses with uncertain numbers.

Abstract

Sensitivity analysis is a study of how changes in the inputs to a model influence the results of the model. Many techniques have recently been proposed for use when the model is probabilistic. This report considers the related problem of sensitivity analysis when the model includes uncertain numbers that can involve both aleatory and epistemic uncertainty and the method of calculation is Dempster-Shafer evidence theory or probability bounds analysis. Some traditional methods for sensitivity analysis generalize directly for use with uncertain numbers, but, in some respects, sensitivity analysis for these analyses differs from traditional deterministic or probabilistic sensitivity analyses. A case study of a dike reliability assessment illustrates several methods of sensitivity analysis, including traditional probabilistic assessment, local derivatives, and a "pinching" strategy that hypothetically reduces the epistemic uncertainty or aleatory uncertainty, or both, in an input variable to estimate the reduction of uncertainty in the outputs. The prospects for applying the methods to black box models are also considered.4

Robust optimization of a dynamic Black-box system under severe uncertainty: A distribution-free framework

“…In this analysis, the epistemic uncertainties are ranked according to the contraction of R(θ base ) resulting from their reduction. This will be done via the adaptive pinching [29] approach outlined in Section 3. The results of the reduced interval R(θ base ) for the respective iteration j for each e ie are illustrated in Figure 13.…”

“…For the computation, we consider the 6 time-slices which were used for the illustration of the P-boxes in Figure 6. To rank the the epistemic parameters according to their respective sensitivity, an adaptive pinching method [29] is proposed to provide a non-empirical approach to determine the pinched bounds of a chosen epistemic parameter which yields the greatest reduction in the value of Ω. The procedure is as follows: For a given i e , the uncertainty space of e ie is reduced by 90 %.…”

A Kaleodoscopic View of Fuzzy Stochastic Optimization*

“…Other approaches to blending epistemic and aleatory forms of uncertainty include imprecise probabilities in the style of Peter Walley [17] and p-boxes defined by Ferson [18]. These approaches may be used to enrich models and methods for Fuzzy Stochastic Optimization.…”

Literature review of methods for representing uncertainty

“…2. probability bound analysis, combining probability analysis and interval analysis Ferson et Tucker 2006;Ferson et al 2007Ferson et al , 2010Moore 1979];…”

“…However, other researchers and analysts have a more positive view on the need for such intervals, see discussions in [Aven et Zio 2011;Ferson et Tucker 2006;Ferson et al 2007Ferson et al , 2010: imprecision intervals are required to reflect phenomena as discussed above, for example when experts are not willing to express their knowledge more precisely than by using probability intervals.…”