Historical context and background

The complexity of exposure assessments necessarily varies, depending on their purpose. Quantitative approaches to exposure assessment have evolved over time as new methodologies have developed, which has led to increasing detail and transparency and the potential for greater harmony in the results obtained from different exposure models. 

In early exposure assessments used in risk characterization, practitioners often used single point estimates of the maximum exposure of individuals to compare with measures of dose-response. Such estimates often lacked transparency in the context of the assumptions on which they were based and led to confusion in terminology (employing concepts such as upper-bound exposure and maximally exposed individual ). 

The historical context of uncertainty estimation in exposure assessment can be traced to the convergence of developments in multiple disciplines. For example, Stanislaw Ulam and John von Neumann are typically credited with creation of the Monte Carlo method for simulation of random events in 1946 (see Metropolis Ulam, 1949 Eckhardt, 1987). However, a paper by Lord Kelvin in 1901 appears to apply concepts similar to Monte Carlo to a discussion of the Boltzmann equation, and there are other precedents (Kelvin, 1901). The modem incarnation of Monte Carlo was first used for prediction of neutron release during nuclear fission and has since been applied in a wide variety of disciplines. 

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