Uncertainty in Risk Analysis : Towards a

| Uncertainty is very important in risk analysis. A natural way to describe this uncertainty is to describe a set of possible values of each unknown quantity (this set is usually an interval), plus any additional information that we may have about the probability of diierent values within this set. Traditional statistical techniques deal with the situations in which we have a complete information about the probabilities; in real life, however, we often have only partial information about them. We therefore need to describe methods of handling such partial information in risk analysis. Several such techniques have been presented, often on a heuristic basis. The main goal of this paper is to provide a justiication for a general second-order formalism for handling different types of uncertainty. I. INTRODUCTION: UNCERTAINTY IN RISK ANALYSIS Uncertainty in risk analysis: why. By deenition, risk analysis deals with situations with uncertainty, i.e., with situations in which we do not have a complete and accurate knowledge about the state of the system. It is therefore very important that we be able to represent uncertainty in risk analysis as adequately as possible. First component of uncertainty description: interval (set) uncertainty. In order to fully describe a system, we must know the exact values of all the physical quantities characterizing this system. For example, in environmental problems related to chemical pollution, a polluted system (e.g., a lake) can be fully described if we know the exact concentration of diierent pollutants in diierent parts of the lake. Thus, to describe the uncertainty of our knowledge about a system, we must describe the uncertainty with which we know the values of each of the quantities (parameters) describing the system. Uncertainty means that we do not know the exact value of the quantity, several diierent values may be possible. For example, we may not know the exact value of the concentration but we may know that this concentration is between, say, 10 ?5 and 10 ?3. In this case, any value from the interval 10 ?5 ; 10 ?3 ] An important risk-related situation that leads to intervals is when a measurement does not detect any presence of a certain substance because its concentration x is below the detection limit D. In this case, the only information we have about x is that x belongs to the interval 0; D]. In general, we usually known an interval x of possible values …