13

Conclusions

The representation and characterization of uncertainties in risk assessment is a serious matter, as uncertainties feature strongly in the decision-making process involved in the management of risk. In looking for a general framework for treating uncertainties in risk assessment, we started with the probabilistic treatment of uncertainties, recognizing its merits and limitations, and thus ventured beyond probability to describe uncertainties in a risk assessment context whose setting demands an extension of concepts and methods. This has led us to consider alternative approaches for representing and characterizing uncertainty, including those based on interval probability, possibility theory, and evidence theory. We have made the point, strongly, that extending the framework for uncertainty analysis naturally leads to extending the framework for risk assessment and management. In much of the existing literature on the representation and analysis of uncertainty, risk is defined in relation to probability. For example, using the well-known triplet definition of risk by Kaplan and Garrick (1981) (see also Kaplan, 1997), risk is equal to the triplet (, , ), where is the i th scenario, the probability of that scenario, and the consequence of the i th scenario, , where is the total number of scenarios. However, if risk is defined through probabilities we need to clarify what probability means. It obviously cannot be a subjective definition, because we seek a general framework that extends beyond such types of probabilities. Hence, probability must refer to a frequentist/propensity concept. However, frequentist probabilities cannot be justified in cases of non-repeatability and therefore cannot serve as a general concept for risk assessment, applicable to all types of uncertainty representations. Consequently, we have to leave the probability-based risk concepts, and extend our considerations to perspectives on risk that are based on uncertainty instead of probability.

One of the most general risk perspectives is the so-called risk perspective, introduced in Section 1.1, where risk is understood as the two-dimensional combination of the (severity of the) consequences of an activity and associated uncertainties (what will be?). This perspective is closely linked to some common risk perspectives in social sciences (Rosa, 1998, 2003; Renn, 2005), which state that risk is basically the same as consequences or events that could lead to . The definitions of risk are different, but when it comes to the way risk is to be described, there are strong similarities as the C -type perspective also covers consequences and uncertainties.

Also, the knowledge dimension needs to enter the scene when we try to describe or measure risk. A risk description is obtained by specifying the consequences and using a description (measure) of uncertainty (which could be probability or any other measure, where measure is here interpreted in a wide sense). Specifying the events/consequences means identifying a set of events/quantities of interest that characterizes the events/consequences . An example of is the number of fatalities. Depending on the principles laid down for specifying and on the choice of , we obtain different perspectives on how to describe/measure risk. As a general description of risk, we can write , where is the knowledge that the specification of and the assignment are based on. Hence, following this definition, there is a sharp distinction between the risk concept per se and how risk is measured or described.

Instead of , we often write when we want to focus on hazards/threats/opportunities A. Similarly we write in place of for the risk description. Vulnerability “given ” can, then, be defined as and a vulnerability description covers : vulnerability given an event is basically risk conditional on this event.

We see that such a way of understanding and describing risk allows for all types of uncertainty representations, and it could consequently serve as a basis of a unified perspective for treating uncertainties in risk assessments.

In this book, we have studied alternative ways of representing and treating the uncertainties in a risk assessment context given this broad understanding of risk. We have looked in five principal directions for the uncertainty representations and treatment:

These directions are not mutually exclusive, because for example direction 4 could be based on a combination of 1 and 2, and 5 could be seen as a special case of 4 since it is based on the combination of a quantitative approach (i.e., direction 1, 2, or 3) and qualitative assessments.

Subjective probability is currently the most common approach for also treating epistemic uncertainty in risk analysis. We have reflected on the position that “probability is perfect” and on the need for an extended framework for risk assessment that reflects the separation that practically exists between analyst and decision maker.

We have argued that we need to see beyond probability to adequately reflect uncertainties in a risk assessment context. The main point raised (see Section 1.5) is the fact that, while probabilities can always be assigned under the subjective probability approach, the origin and amount of information supporting the assignments are not reflected by the numbers produced.

However, how we should see beyond probability is not straightforward. A handful of approaches are available, but they are not easily implemented in practice. More research has to be carried out to bring these alternative approaches to an operative state where they can in fact be used in practice, when needed. The development in this direction should have the clear aim of obtaining a unified perspective (covering concepts, principles, theories, and operative approaches) for the representation and characterization of risk and uncertainty, by linking probability and alternative representations of uncertainty. The present book is to be seen as an attempt to provide a basis for such a work and describe current thinking about these issues.

A framework for risk assessment needs to allow for both qualitative and quantitative approaches. Earlier work has to a large extent been quantitative, but we have underlined that the full scope of the risks and uncertainties cannot be transformed into a mathematical formula, using probabilities or other quantitative measures of uncertainty. Numbers can be generated, but these alone would not serve the purpose of the risk assessment: to reveal and describe the risks and uncertainties. Some qualitative approaches linked to probability exist (see Section 7.5), but similar approaches have not been developed for the alternative quantitative approaches (probability-bound analysis, imprecise probabilities, possibility theory, evidence theory).

Finally, earlier attempts at integration (e.g., hybrid probability and possibility approaches) have been based on the idea that there exists one and only one appropriate representation in a specific case (e.g., possibility representation if the information is poor and subjective probabilities if the information is strong). We believe that the variety of decision-making situations calls for a unified perspective that allows the use of several approaches for representing and characterizing the risk and uncertainties. To inform the decision maker, both subjective probabilities and imprecision intervals may be used, as these approaches could capture different types of information and knowledge important for the decision maker. In addition, qualitative approaches could be incorporated to provide an even more nuanced characterization of the risk and uncertainties.

The “non-probabilistic methods” are also based on a set of premises and assumptions, but not to the same degree as the pure probability-based analyses. Their motivation is that the intervals produced correspond better to the information available. A hybrid probability–possibility analysis may result in an interval (say) for a subjective probability . The risk analysts (experts) are not able or willing to precisely assign their probability . The decision maker may, however, request that the analysts make such assignments – the decision maker would like to be informed of the analysts' degree of belief. The analysts are consulted as experts in the field studied and the decision maker expects them to give a faithful report on the epistemic uncertainties about the unknown quantities addressed. The decision maker knows that these judgments are based on some knowledge and some assumptions, and are subjective in the sense that others could conclude differently, but these judgments are still considered valuable as the analysts have competence in the field being studied. They are trained in probability assignments and the decision maker expects that they will be able to transform their knowledge into probability figures.

Our experience, based on many years of work with risk assessment methodologies and applied risk assessments, is that engineers and risk analysts often struggle with the uncertainty analysis part. We hope that this book can provide some help and guidance. However, the book is not a cookbook for how to conduct uncertainty analysis in a risk assessment context; what is covered are the basic ideas, concepts, and some methods for a set of alternative approaches, as well as overall reflections on how to think when addressing uncertainty in these contexts. The theory, together with the examples presented and discussed in the book, should give the reader a solid basis for these topics and serve well as preparation for carrying out uncertainty analyses in practice.