An Introduction to Second-Order Random Variables in Human Health Risk Assessments

When performing a human health risk assessment using probabilistic methods, risk assessors need a way to distinguish, analyze, and visualize both the variability and the uncertainty in a quantity. As described by many previous authors, first-order random variables represent variability, i.e., the heterogeneity or diversity in a well-characterized population which is usually not reducible through further measurement or study. Growing in popularity, second-order random variables also include uncertainty, i.e., partial ignorance or lack of perfect knowledge about a poorly characterized phenomenon which may be reducible through further study. In this manuscript, we explore second-order random variables as a way to encode and propagate variability and uncertainty separately.