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Uncertainties in parameter values arise for three reasons. First, the value may have been measured, in which case some imprecision is associated with the process of measurement. In the context of this report, however, errors of measurements are likely to be insignificant compared to other kinds of uncertainty. Second, the value may have been measured, but under circumstances other than those for which it must be applied. In this case, additional uncertainty arises from the variation of the parameter in time and space. Third, the value may not have been measured at all, but estimated from relationships with other quantities that are known or measured. In this case, uncertainty in the parameter of interest arises form both uncertainty in the quantities that are measured and from uncertainty about the estimating relationship.

By characterizing the uncertainties in the input parameters of a model and studying the effects of variation in these parameters on the model predictions, we can estimate the part of the uncertainty in the predictions that is due to uncertainty in the inputs.

Uncertainty can be characterized by a probability distribution. That is, the value of a parameter is not known exactly, but, for example, it might be thought to lie between 90 and 100 with probability 0.5, between 85 and 120 with probability 0.75, and so on. Sometimes such probability distributions can be usefully summarized by a few parameters, such as the mean and standard deviation. Uncertainties in the input parameters propagate through the model to produce probability distributions on the output parameters. Figure 1 presents a schematic description of the uncertainty propagation through a model.

We present here a structured methodology for the parameter uncertainty analysis of health risk estimates. The methodology involves: (1) a sensitivity analysis of the model used to perform the health risk calculations, (2) the determination of probability distributions for a number of selected input parameters (i.e., the ones identified as the most influential to the output variable); and (3) the propagation of the uncertainties through the model.

This methodology is applied here to the uncertainty analysis of the carcinogenic health risks estimated as due to the emissions of a coal-fired plant.

Uncertainty Analysis Methodology

Overview

A health risk assessment model combines a number of models to simulate the transport and fate of chemicals in air, surface water, surface soil, groundwater and the foodchain. Concentrations calculated by the fate and transport models



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