Uncertainty Analysis When Separation of Uncertainties Is Required

Abstract

This chapter is not about how to do an uncertainty analysis that quantifies aleatoric uncertainty. Instead it explains, for each of the six analysis steps discussed in Chaps. 2–7, how to proceed with the analysis of the epistemic uncertainties if the computer model also operates with aleatoric uncertainties and the combined effect of the latter is the actual model result. Differences to the case of only epistemic uncertainties are explained step by step. In Step 1, the uncertain parameters of the stochastic models, quantifying the aleatoric uncertainties, need to be identified. In Step 2, their state of knowledge is to be quantitatively expressed by subjective probability distributions. The most prominent difference lies in Step 3 (propagate) where the simulation will need to proceed with two nested sampling loops if the analysis of the aleatoric uncertainties is not already taken care of by the computer model. Distribution functions, quantifying the aleatoric uncertainty, and probabilities (in the classical interpretation) that may be read from those distributions are among the model results. In Step 4, it will be necessary to obtain quantitative expressions of their epistemic uncertainty. Importance measures will need to be computed for the aleatoric uncertainties in the inner simulation loop and for the epistemic uncertainties in the outer loop in Step 5. The epistemic uncertainty of the former importance measures will also be of interest. Step 6 then shows ways of how to present the information obtained on both simulation levels.