How to Deal with Uncertainty Quantification and Propagation

Abstract

Over the last years, stochastic models have called the attention of researchers. The number of publications in the subject has grown and the topic is being analyzed in different applications. Observing the new literature produced in the field, it is possible to verify that new expressions, as uncertainty quantification and uncertainty propagation, have emerged. These expressions become largely used and fashionable, however there is no consensus of their meanings. Each author arbitrates a meaning according to its own convenience. Sometimes the disarray is such that different meanings, some of them contradictory, can be found throughout the same work. The objective of this paper is to clarify the concepts. We define what is and what is not uncertainty quantification and propagation. We also show, with simple examples, that several strategies found in literature called strategies to compute uncertainty quantification and propagation are not. They can lead to errors and misleadingness. The examples were chosen to be as simple as possible in order to highlight different problems that can arise when one uses these strategies.