Estimating Distributions for Cleanup Targets, D. E. Burmaster, Alceon Corporation, PO Box 2669, Cambridge, MA 02238-2669
For each pathway in a public health risk assessment for carcinogens in contaminated soils, an analyst combines data and assumptions about the exposure to chemicals and about the toxicity of the chemicals to estimate the risk to the person or population exposed. In a probabilistic risk assessment, the analyst combines a set of distributions representing the variability and the uncertainty in the input variables to estimate a distribution of risk as the output. In a probabilistic assessment, the analyst cannot re-arrange the algebraic equation in the deterministic fashion to backcalculate a distribution for the target cleanup concentration from distributions for acceptable risk and the other variables. As a simple example, let a, b, c, d, e, and f be positive random variables as inputs for calculating Risk as the output. For distributions, the equation Risk = ( a · b · c · d ) / ( e · f ) cannot be inverted to recover the distribution for variable "a" from knowledge of Risk, b, c, d, e, and f. In other words, a =! = ( Risk · e · f ) / ( b · c · d ) for distributions. This counter-intuitive result shows that it is incorrect to estimate the distribution for the target cleanup concentration using a Monte Carlo program to simulate the distribution of an inverted equation. We will discuss mathematically correct methods to estimate distributions for cleanup targets and the implications of these results in risk management decisions.