Mechanistic modeling of physical systems is often complicated by the presence of uncertainties. Environmental and biological modeling, for example, entails uncertainties in the estimates of toxicant emissions, transformation and transport parameters, etc., that impact the estimates of related health risks. The implications of these uncertainties are particularly important in the assessment of several potential regulatory options, for example, with respect to the selection of a strategy for the control of pollutant levels. Even though significant effort may be needed to incorporate uncertainties into the modeling process, this could potentially result in providing useful information that can aid in decision making.
A systematic uncertainty analysis provides insight into the level of confidence in model estimates, and can aid in assessing how various possible model estimates should be weighed. Further, it can lead to the identification of the key sources of uncertainty (such as data gaps) which merit further research, as well as the sources of uncertainty that are not important with respect to a given response.
The purpose of quantitative uncertainty analysis is to use currently available information in order for quantifying the degree of confidence in the existing data and models. The purpose is not to somehow ``reduce'' uncertainty - reduction in uncertainty can only come from gathering additional information and filling ``data gaps''. Even though the applicability of a model is limited by the model assumptions and the uncertainties in the evaluation data, understanding the judgments associated with the modeling process is more valuable than side-stepping the uncertainty analysis. In fact, it is precisely for problems where data are limited and where simplifying assumptions have been used that a quantitative uncertainty analysis can provide an illuminating role, to help identify how robust the conclusions about model results are, and to help target data gathering efforts [72].
The following stages are involved in the uncertainty analysis of a model: (a) estimation of uncertainties in model inputs and parameter ( characterization of input uncertainties), (b) estimation of the uncertainty in model outputs resulting from the uncertainty in model inputs and model parameters (uncertainty propagation), (c) characterization of uncertainties associated with different model structures and model formulations (characterization of model uncertainty), and (d) characterization of the uncertainties in model predictions resulting from uncertainties in the evaluation data.