A Critical Discussion and Practical Recommendations on Some Issues Relevant to the Nonprobabilistic Treatment of Uncertainty in Engineering Risk Assessment.

Models for the assessment of the risk of complex engineering systems are affected by uncertainties due to the randomness of several phenomena involved and the incomplete knowledge about some of the characteristics of the system. The objective of this article is to provide operative guidelines to handle some conceptual and technical issues related to the treatment of uncertainty in risk assessment for engineering practice. In particular, the following issues are addressed: (1) quantitative modeling and representation of uncertainty coherently with the information available on the system of interest; (2) propagation of the uncertainty from the input(s) to the output(s) of the system model; (3) (Bayesian) updating as new information on the system becomes available; and (4) modeling and representation of dependences among the input variables and parameters of the system model. Different approaches and methods are recommended for efficiently tackling each of issues (1)-(4) above; the tools considered are derived from both classical probability theory as well as alternative, nonfully probabilistic uncertainty representation frameworks (e.g., possibility theory). The recommendations drawn are supported by the results obtained in illustrative applications of literature.

Estimating hazardous concentrations by an informative Bayesian approach.

The species sensitivity distribution (SSD) approach is recommended for assessing chemical risk. In practice, however, it can be used only for the few substances for which large-scale ecotoxicological results are available. Indeed, the statistical frequentist approaches used for building SSDs and for deriving hazardous concentrations (HC5) inherently require extensive data to guarantee goodness-of-fit. An alternative Bayesian approach to estimating HC5 from small data sets was developed. In contrast to the noninformative Bayesian approaches that have been tested to date, the authors' method used informative priors related to the expected species sensitivity variance. This method was tested on actual ecotoxicological data for 21 well-informed substances. A cross-validation compared the HC5 values calculated using frequentist approaches with the results of our Bayesian approach, using both complete and truncated data samples. The authors' informative Bayesian approach was compared with noninformative Bayesian methods published in the past, including those incorporating loss functions. The authors found that even for the truncated sample the HC5 values derived from the informative Bayesian approach were generally close to those obtained using the frequentist approach, which requires more data. In addition, the probability of overestimating an HC5 is rather limited. More robust HC5 estimates can be practically obtained from additional data without impairing regulatory protection levels, which will encourage collecting new ecotoxicological data. In conclusion, the Bayesian informative approach was shown to be relatively robust and could be a good surrogate approach for deriving HC5 values from small data sets.