Probabilistic Risk Analyses: NRC Programs and Perspectives

The historical basis and more recent activities and products of probabilistic risk analysis (PRA) in the Atomic Energy Commission and Nuclear Regulatory Commission (NRC) are reviewed. Current NRC program activities and objectives are described. The author's opinions on the best uses of PRA are presented.     

Using the Biological Two-Stage Model to Assess Risk from Short-Term Exposures

Two assumptions used in risk assessment are investigated: (1) the assumption of fraction of lifetime dose rate assumes that the risk from a fractional lifetime exposure at a given dose rate is equal to the risk from full lifetime exposure at that same fraction of the given dose rate; (2) the assumption of fraction of lifetime risk assumes that the risk from a fractional lifetime exposure at a given dose rate is equal to that same fraction of the risk from full lifetime exposure at the same dose rate. These two assumptions are equivalent when risk is a linear function of dose. Thus both can be thought of as generalizations of the assumption that cancer risk is proportional to the total accumulated lifetime dose (or average daily dose), which is often made to assess the risk from short-term exposures. In this paper, the age-specific cumulative hazard functions are derived using the two-stage model developed by Moolgavkar, Venzon, and Knudson for situations when the exposure occurs during a single period or a single instant. The two assumptions described above are examined for three types of carcinogens, initiator, completer, and promoter, in the context of the model. For initiator and completer, these two assumptions are equivalent in the low-dose region; for a promoter, using the fraction of lifetime risk assumption is generally more conservative than that of the fraction of lifetime dose rate assumption. Tables are constructed to show that the use of either the fraction of lifetime dose rate assumption or the fraction lifetime risk assumption can both underestimate and overestimate the true risk for the three types of carcinogens.     

Empirical Bayes rules and Gaussian processes

In this paper we study empirical Bayes (e.B.) rules from a viewpoint which has not yet got any attention in the literature. Since an e.B. estimator can be seen as an estimate of an unknown function, namely the true Bayes estimator, it is natural to consider e.B. estimators as stochastic processes. In this paper we make a first attempt in the direction of this approach. For a certain class of e.B. estimators for the continuous one-parameter exponential family, we investigate the global behaviour on finite intervals. It is shown that the difference between the e.B. and the true Bayes estimator can be represented as a certain type of Gaussian process plus a remainder which is uniformly of smaller order. Several applications of this result are given.     

Judgment and Analysis in Oil Spill Risk Assessment

The risk of oil spills is a major environmental issue in the siting of proposed coastal refineries, oil terminals, deepwater ports, and in the leasing of offshore lands for oil exploration and development. As with any kind of risk, oil spill risk assessment is inherently judgmental and no analytic method can eliminate the need for judgment. This paper compares representative examples of oil spill risk assessments with regard to decisions about data, variables, functional relations, and uncertainty. The comparison emphasizes the judgmental basis of analytic methods.     

Issues in Qualitative and Quantitative Risk Analysis for Developmental Toxicology1

The qualitative and quantitative evaluation of risk in developmental toxicology has been discussed in several recent publications.(^1–3) A number of issues still are to be resolved in this area. The qualitative evaluation and interpretation of end points in developmental toxicology depends on an understanding of the biological events leading to the end points observed, the relationships among end points, and their relationship to dose and to maternal toxicity. The interpretation of these end points is also affected by the statistical power of the experiments used for detecting the various end points observed. The quantitative risk assessment attempts to estimate human risk for developmental toxicity as a function of dose. The current approach is to apply safety (uncertainty) factors to die no observed effect level (NOEL). An alternative presented and discussed here is to model the experimental data and apply a safety factor to an estimated risk level to achieve an “acceptable” level of risk. In cases where the dose-response curves upward, this approach provides a conservative estimate of risk. This procedure does not preclude the existence of a threshold dose. More research is needed to develop appropriate dose-response models that can provide better estimates for low-dose extrapolation of developmental effects.     

Lorenz non-consistent welfare and inequality measurement

Typical welfare and inequality measures are required to be Lorenz consistent which guarantees that inequality decreases and welfare increases as a result of a progressive transfer. We explore the implications for welfare and inequality measurement of substituting the weaker absolute differentials and deprivation quasi-orderings for the Lorenz quasi-ordering. Restricting attention to distributions of equal means, we show that the utilitarian model - the so-called expected utility model in the theory of risk - does not permit one to make a distinction between the views embedded in the differentials, deprivation and Lorenz quasi-orderings. In contrast it is possible within the dual model of M. Yaari (Econometrica 55 (1987), 99–115) to derive the restrictions to be placed on the weighting function which guarantee that the corresponding welfare orderings are consistent with the differentials and deprivation quasi-orderings respectively. Finally we drop the equal mean condition and indicate the implications of our approach for the absolute ethical inequality indices.     

Mutual-Fund Benchmarking and Market Bubbles: A Behavioral Approach

Dynamics of equity risk premium is not directly measurable on the market. Numerous studies and empirical research analyse its volatility also considering the time span, concluding that the dynamics of equity risk premium over time is inversely proportional to the economic cycle. This study analyses the passive role that, implicitly, would place institutional investors in such a context. In reality, savings management is delegated to a small number of professional operators (institutional investors), as opposed to pure theoretical models in which every person can act directly on the market thus ensuring unlimited price elasticity. Institutional investors should be rational and completely informed so that they can assume an anticyclical position on the market. Thus, supply and demand should quickly smooth over emerging price pressures and avoid price bubbles. We analyse one possible explanation for this situation not to occur, namely, that professionals suffer from operational limits that prevent them from doing their job in the best possible way. Using empirical evidence from the Italian Stock Exchange (Comit Index), we conclude that three factors reduce the freedom of institutional investors to manage their portfolios – the market target size, the fund structure, and the benchmarking – and discuss some implications for each of them.     

On Loss Distributions from Installment-Repaid Loans

The banks have been accumulating huge data bases for many years and are increasingly turning to statistics to provide insight into customer behaviour, among other things. Credit risk is an important issue and certain stochastic models have been developed in recent years to describe and predict loan default. Two of the major models currently used in the industry are considered here, and various ways of extending their application to the case where a loan is repaid in installments are explored. The aspect of interest is the probability distribution of the total loss due to repayment default at some time. Thus, the loss distribution is determined by the distribution of times to default, here regarded as a discrete-time survival distribution. In particular, the probabilities of large losses are to be assessed for insurance purposes.     

A New Look at the Psychometric Paradigm of Perception of Hazards

The psychometric paradigm has been the most influential model in the field of risk analysis. The "cognitive maps" of hazards produced by the paradigm seem to explain how laypeople perceive the various risks they face. Because most of the studies used aggregated data, analyzed using principal component analysis, it is not known whether the model neglects individual differences in risk perception. There has been much criticism on the fact that few studies have examined individual differences in the cognitive representation of hazards. In order to detect and describe the internal structure of the three-way data, we conducted a three-way component analysis (3MPCA). Data for the present analysis were derived from a mail survey conducted in Switzerland. Participants were asked to judge 9 attributes for 26 hazards. Individual differences in the cognitive representation of hazards were correlated with external variables (e.g., general trust). The results suggest that methods permitting individual differences should be used more frequently and that utilizing different methods could provide greater insight into the cognitive representation of risks.