fully is to perform a two-dimensional Monte Carlo simulation consisting of an inner set of calculations embedded within an outer set. That was first described by Bogen and Spear (1987).
One of the issues that must be confronted in uncertainty analysis is how to distinguish between the relative contributions of variability (heterogeneity) and true uncertainty (measurement precision) to the characterization of predicted outcome. Variability refers to quantities that are distributed empirically—such factors as rainfall, soil characteristics, weather patterns, and human characteristics that come about through processes that we expect to be stochastic because they reflect actual variations in nature. These quantities are inherently random or variable and cannot be represented by a single value, so we can determine only their characteristics (mean, variance, skewness, and so on) with precision. In contrast, true uncertainty, or model-specification error (such as statistical estimation error), refers to an input that, in theory, has a single value, which cannot be known with precision because of measurement or estimation error.
Uncertainty in model predictions arises from a number of sources, including specification of the problem, formulation of the conceptual model, estimation of input values, and calculation, interpretation and documentation of the results. Of the factors that determine precision and accuracy, only uncertainties due to estimation of input values can be quantified in a straightforward manner on the basis of variance propagation techniques. Uncertainties that arise from mis-specification of the problem and model-formulation errors can be assessed using less straightforward processes, such as decision trees and event trees based on expert opinions. In some cases, using such methods as meta-analysis, model-specification errors can be handled with simple variance-propagation methods.
In support of its proposed rule for radionuclides in drinking water, EPA has developed estimates of the cancer risk associated with radon in drinking water. The risk arises from multiple exposure pathways, including the direct ingestion of water that contains radon, the inhalation of indoor air that contains radon some of which has volatilized from water used in the home, and the inhalation of radon progeny that are introduced into indoor air as a result of radon decay. Because exposure and dosimetry are different for each pathway, EPA has estimated the risks associated with radon in drinking water by calculating the risk for each pathway separately and then combining risk to obtain the total risk related to all pathways. In an earlier risk assessment (EPA 1995), EPA estimated the total (all-pathways) average lifetime risk to the US population posed by radon in drinking water as 6.6 × 10-7 per picocurie per liter of radon in water.
After the risk estimates were performed, EPA obtained new data on radiation dosimetry that required revision of the estimates for radon in drinking water. The