Monte Carlo modeling with uncertain probability density functions

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Abstract
Monte Carlo modeling is a powerful mathematical technique that offers many advantages compared to traditional point estimate methods for characterizing the inherent variability in exposure to environmental chemicals among different members of a population. However, Monte Carlo analyses of variability are often limited by uncertainty (lack of knowledge) about the true distribution of key exposure and risk parameters. Because of this uncertainty, it is not appropriate to select only one value (either a “best estimate” or, even worse, an intentionally conservative value) for each uncertain parameter, because the result of a simulation employing such fixed point estimates is only one of many possible results that could be true. The solution to this problem is to run repeated Monte Carlo simulations, using different combinations of the uncertain parameters as inputs. The degree of variation between the output of different simulations then reveals how certain (or how uncertain) any particular estimate (e.g., mean, 95th percentile) of exposure or risk may be. This type of information maximizes the opportunity for risk managers to make informed decisions.