Different methods are needed to propagate ignorance and variability

There are two kinds of uncertainty. One kind arises as variability resulting from heterogeneity or stochasticity. The other arises as partial ignorance resulting from systematic measurement error or subjective (epistemic) uncertainty. As most researchers recognize, variability and ignorance should be treated separately in risk analyses. Although a second-order Monte Carlo simulation is commonly employed for this task, this approach often requires unjustified assumptions which may be inappropriate in some circumstances. We argue that the two kinds of uncertainty should be propagated through mathematical expressions with different calculation methods. Basically, interval analysis should be used to propagate ignorance, and probability theory should be used to propagate variability. We demonstrate how using an inappropriate method can yield erroneous results. We also show how ignorance and variability can be represented simultaneously and manipulated in a coherent analysis that does not confound the two forms of uncertainty and distinguishes what is known from what is assumed.