Introduction

Suppose we have constructed a model to predict the consequences of various possible events and decisions. And suppose further we have identified various uncertainties in the inputs. How can we propagate these uncertainties through the model to discover the uncertainty in the predicted consequences? If the uncertainties are substantial, we may not immediately be able to make definitive recommendations about what decision is “best.” But we should be able to obtain useful insights about the relative importance to our conclusions of the various assumptions, decisions, uncertainties, and disagreements in the inputs. These can help us decide whether it is likely to be worthwhile gathering more information, making more careful uncertainty assessments, or refining the model, and which of these could most reduce the uncertainty in the conclusions. In this chapter, we examine various analytic and computational techniques for examining the effects of uncertain inputs within a model. These include:

• methods for computing the effect of changes in inputs on model predictions, i.e., sensitivity analysis,

• methods for calculating the uncertainty in the model outputs induced by the uncertainties in its inputs, i.e., uncertainty propagation, and

• methods for comparing the importance of the input uncertainties in terms of their relative contributions to uncertainty in the outputs, i.e., uncertainty analysis.

A considerable variety of such methods have been developed, with wide differences in conceptual approach, computational effort required, and the power of their results.