Assessment of Variability and Uncertainty Distributions for Practical Risk Analyses

Abstract

In recent years the U.S. Environmental Protection Agency has been challenged both externally and internally to move beyond its traditional conservative single-point treatment of various input parameters in risk assessments. In the first section, we assess when more involved distribution-based analyses might be indicated for such common types of risk assessment applications as baseline assessments of Superfund sites. Then in two subsequent sections, we give an overview with some case studies of technical analyses of (A) variabilityheterogeneity and (B) uncertainty. By "interindividual variability" is meant the real variation among individuals in exposure-producing behavior, in exposures, or some other parameter (such as differences among individual municipal solid waste incinerators in emissions). In contrast, "uncertainty" is a description of the imperfection in knowledge of the true value of a particular parameter or its real variability in an individual or a group. In general uncertainty is reducible by additional information-gathering or analysis activities (better data, better models), whereas real variability will not change (although it may be more accurately known) as a result of better or more extensive measurements. The purpose of the rather long-winded exposition of these two final sections is to show the differences between analyses of these two different things, both of which are described using the language of probability distributions.

Statistical Sampling for In-Service Inspection of Liquid Waste Tanks at the Savannah River Site

“…Lognormal distributions have a central role in risk assessment. Many physical, chemical, biological, toxicological, and statistical processes tend to create random variables that follow lognormal distributions 4 . A variable X is lognormally distributed if Y = ln(X) is normally distributed ("ln" denotes the natural logarithm, log base 10 is also used).…”

Uncertainties of a Regional Terrestrial Biota Full Carbon Account: A Systems Analysis

“…Albeit the term uncertainty is used in different meanings: statistical variability, lack of knowledge, lack of confidence in a single value (Hattis and Burmaster, 1994;Heath and Smith, 2000;Hofman and Hommonds, 1994), the use of this term in global change science is rather consistent.…”

“…The comprehensive development of the formal theory, which would provide for learning about natural fuzzy systems is, to a significant extent, a matter for the future. Although fuzzy logic and fuzzy methods are recommended as a means to incorporate subjective information in different aspects of assessing uncertainties (e.g., Haimes et al, 1994;Hattis and Burmaster, 1994), their applications in ecology and natural management are limited by numerous and diverse but partial tasks (Mendoza and Sprouse, 1989;Bare and Mendoza, 1991;Wan-Xiong et al, 2003;Chen and Mynett, 2003;Özesmi and Özesmi, 2004 etc.). In the framework of FCA, it is productive to apply "fuzzy thinking", a philosophical approach, which helps much in structuring problems, developing a relevant FCA system and treating uncertainties.…”

Quantification of Variability and Uncertainty in Air Pollutant Emission Inventories: Method and Case Study for Utility NOxEmissions

“…Discussions of distribution selection criteria can be found elsewhere. 17,[22][23][24][25] Once a particular parametric distribution has been selected, a key step is to estimate the parameters of the distribution. The method of maximum likelihood estimation (MLE) and the method of matching moments are among the most typical techniques used for estimating the parameters.…”