Uncertainty quantification: Methods and examples from probability and fuzzy theories

Uncertainties arise from many sources: random effects, measurement errors, modeling choices, parameter choices, inference processes, application of expertise, decision making, and lack of knowledge, to name a few. Characterizing or estimating these is often a daunting task, involving the gathering and analysis of data, knowledge and information. Often this information is in qualitative form, and often the source is from human experience and cognitive processes. Because uncertainty is a broadly encompassing topic, we will provide some definitions to focus the issues and present a philosophy with some guidelines for understanding and handling uncertainties of specific types. As part of that philosophy, we recommend formal expert elicitation and analysis methods for estimating, quantifying and propagating uncertainties through a complex problem. Some examples are presented illustrating some of the aspects in quantifying uncertainties of various types.