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

Abstract

An 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.

Keywords:

• epistemic uncertainty
• risk analysis
• uncertainty propagation
• decision-making

Acknowledgement

This work was supported by the CO₂ Programme of the French National Research Agency (ANR; project CRISCO2, N° ANR-06-CO2-003).

Notes

^1. A random disjunctive set, in fact. There is a branch of random set theory (Kendall 1974) where the set-valued realisations represent objective entities (e.g. a shape to be located in some area). In contrast, in this paper, set-valued realisations are epistemic constructs representing incomplete information.