Risk-informed decision-making in the presence of epistemic uncertainty

Abstract

International audienceAn important issue in risk analysis is the distinction between epistemic and aleatory uncertainties. In this paper, the use of distinct representation formats for aleatory and epistemic uncertainties is advocated, the latter being modelled by sets of possible values. Modern uncertainty theories based on convex sets of probabilities are known to be instrumental for hybrid representations where aleatory and epistemic components of uncertainty remain distinct. Simple uncertainty representation techniques based on fuzzy intervals and p-boxes are used in practice. This paper outlines a risk analysis methodology from elicitation of knowledge about parameters to decision. It proposes an elicitation methodology where the chosen representation format depends on the nature and the amount of available information. Uncertainty propagation methods then blend Monte-Carlo simulation and interval analysis techniques. Nevertheless, results provided by these techniques, often in terms of probability intervals, may be too complex to interpret for a decision-maker and we therefore propose to compute a unique indicator of the likelihood of risk, called confidence index. It explicitly accounts for the decision-maker's attitude in the face of ambiguity. This step takes place at the end of the risk analysis process, when no further collection of evidence is possible that might reduce the ambiguity due to epistemic uncertainty. This last feature stands in contrast with the Bayesian methodology, where epistemic uncertainties on input parameters are modelled by single subjective probabilities at the beginning of the risk analysis process

HYRISK: An R package for hybrid uncertainty analysis using probability, imprecise probability and possibility distributions

“…Results of the hybrid uncertainty propagation step for the dike stability case; the black and red lines respectively represent the lower and upper probability distribution, which defines the p-box related to the uncertainty on Z. The green and blue lines respectively represent the probability distribution determined by a weighing averaging of both bounds, here using a weight of 30 and 50% (following the approach of (Dubois and Guyonnet 2011)). …”

“…As described in the introduction, depending on the available data and information and on the nature of the model parameter, the most appropriate mathematical tools and procedures should be selected (Dubois and Guyonnet 2011). The HYRISK package provides a broad range of different mathematical representation tools to handle different uncertainty situations.…”

“…Therefore, to overcome the shortcomings of the classical probabilistic setting, several alternative mathematical representation methods have been developed: e.g., probability boxes, possibility distributions, Dempster-Shafer structures, etc. (see an overview by Dubois and Guyonnet (2011)). …”

“…(Ferson 1996;Helton, Johnson, and Oberkampf 2004;Baudrit 2005;Baudrit and Dubois 2006;Baudrit et al 2007;Dubois and Guyonnet 2011;Beer, Ferson, and Kreinovich 2013). In such highly uncertain situations, the challenge is to formulate appropriate mathematical tools and models in a quantitative manner, on the one hand, accounting for all data and pieces of information, but, on the other hand, without introducing unwarranted assumptions (Beer et al 2013).…”

Discriminating thresholds as a tool to cope with imperfect knowledge in multiple criteria decision aiding: Theoretical results and practical issues

“…The ordered structures with one or two thresholds are of a particular interest in decision aiding for modeling the imperfect knowledge (Jacquet-Lagrèze, 1975;Vincke, 1984, 1987;Bouyssou, 1989;Roy, 1989;Smets, 1991;Dubois and Guyonnet, 2011).…”