Uncertainty vs. variability: what's the difference and why is it important?

Abstract

Technical professionals are often asked to estimate “ranges” for uncertain quantities. It is important that they distinguish whether they are being asked for variability ranges or uncertainty ranges. Likewise, it is important for modelers to know if they are building models of variability or uncertainty, and their relationship, if any. We discuss and clarify the distinction between uncertainty and variability through strict definition, illustrative analogy and numerical examples. Uncertainty means we do not know the value (or outcome) of some quantity, eg the average porosity of a specific reservoir (or the porosity of a core-sized piece of rock at some point within the reservoir). Variability refers to the multiple values a quantity has at different locations, times or instances - eg the average porosities of a collection of different reservoirs (or the range of core-plugs porosities at different locations within a specific reservoir). Uncertainty is quantified by a probability distribution which depends upon our state of information about the likelihood of what the single, true value of the uncertain quantity is. Variability is quantified by a distribution of frequencies of multiple instances of the quantity, derived from observed data. That both are represented by ‘distributions’ is a major source of confusion, which can lead to uncritical adoption of frequency distributions to represent uncertainty, and thus to erroneous risk assessments and bad decisions. For example, the variability of natural phenomena is sometimes well-approximated by normal or log-normal distributions, but such distributions may not be appropriate to represent the uncertainty in outcome of a single occurrence. We show there is no objectively ‘right’ probability distribution for quantifying the uncertainty of an unknown event – it can only be ‘right’ in that it is consistent with the assessor’s information. Thus, different people (or teams or companies) can legitimately hold different probabilities for the same event. Only in very restrictive, arguably unrealistic, situations can we choose to use a frequency distribution derived from variability data as a probability distribution to represent our uncertainty in an event’s outcome. Our experience as educators of students and oil & gas industry personnel suggests that significant confusion exists in their understanding of the distinction between variability and uncertainty. This paper thus provides a resource for technical professionals and teachers to clarify the distinction between the two, or to correct it where it has been wrongly taught, and thereby help to improve decision-making.