A Computational Alternative to Second-Order Monte Carlo Simulation for Propagation of Variability and Uncertainty in Exposure Assessments. S. Ferson, Applied Biomathematics, 100 North Country Road, Setauket, NY 11733; and R. C. Lee, Golder Associates Inc., 4104 148th Avenue NE, Redmond, WA 98052
Much recent interest has been focused on the use of second order simulation methods (i.e. "two dimensional Monte Carlo" or "nested loop Monte Carlo") for propagation of parameter uncertainties in risk assessment models. This method is computationally intensive and is only suitable for parametric uncertainty about an input’s distribution. When the distribution family itself is unknown, this method can become very cumbersome. Although second-order methods are intended to distinguish stochastic variability and uncertainty associated with the state of knowledge, they often yield results that cannot be justified by appeal to empirical information by treating both with the same methods. Additionally, it is difficult to assess model uncertainty, to perform backcalculations, and to incorporate temporal changes in simulations using this method. Probability bounds arithmetic is an alternative method that addresses many of these shortcomings. An example is presented based on modifications to an EPA model used to assess toxicant exposures from waste incinerator emissions. The specific exposure pathway is ingestion of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) through home-grown beef. Results are compared to a previously published second-order Monte Carlo analysis of this exposure scenario. The probability bounds method results in a wider range of uncertainty associated with exposure than the Monte Carlo method. Limitations of the probability bounds method are discussed. Recommendations are made regarding stochastic modeling approaches to complex environmental problems based on this comparison.