Uncertainty: its statistical meaning and treatment

© 2004-2005 William Charteris
www.billcharteris.com
www.imperialconsulting.net

The term ‘uncertainty’ is normally used to describe a lack of sureness about something or someone, ranging from just short of complete sureness to an almost complete lack of conviction about an outcome. ‘Doubt’, ‘dubiety’, ‘skepticism’, ‘suspicion’, and ‘mistrust’ are common synonyms. Each synonym expresses an aspect of uncertainty that plays a part in risk analysis. Uncertainty with respect to natural phenomena means that an outcome is unknown or not established and is therefore in question. Uncertainty with respect to a belief means that a conclusion is not proven or is supported by questionable information. Uncertainty with respect to a course of action means that a plan is not determined or is undecided. In many, but not all, situations a lack of sureness can be described statistically by probability distributions. The term ‘uncertainty’ is used to describe situations without sureness, whether or not described by a probability distribution.

Uncertainty is at the heart of the scientific method. Scientific uncertainty typically results from five characteristics of the scientific method: the variable chosen, the measurements made, the samples drawn, the models used, and the causal relationship employed. Scientific uncertainty may also arise from a controversy on existing data or lack of some relevant data. Uncertainty may relate to qualitative or quantitative elements of the analysis.

Generally speaking, uncertainty can be attributed to two sources: (i) the inherent variability of natural processes (“natural variability”), or (ii) incomplete knowledge (“knowledge uncertainty”). The ‘flux of nature’ is a metaphor for ‘natural variability’. ‘Natural variability’, sometimes called ‘aleatory uncertainty’, pertains to the inherent variability in the physical world; and, by assumption, this “randomness” is irreducible. The word ‘aleatory’ comes from the Latin alea, meaning a die or gambling device. In a food safety context, uncertainties related to natural variability include things such as microbial mutation, assumed to be a random process in time, or microbial distribution, assumed to be random in space. Natural variability is also sometimes referred to as external, objective, random, or stochastic uncertainty. ‘Knowledge uncertainty’, sometimes called ‘epistemic uncertainty’, pertains to a lack of understanding of events and processes, or with a lack of data from which to draw inferences; and, by assumption, such lack of knowledge is reducible with further information. The word ‘epistemic’ is derived from the Greek “to know.” Knowledge uncertainty is also sometimes referred to as functional, internal, or subjective uncertainty.

‘Natural variability’ and ‘Knowledge uncertainty’ arise for different reasons and are usually evaluated in different ways. A personal simplistic illustration of the distinction between the two sources of uncertainty involves a response surface model, in which the model describes natural variability, and the associated error bounds about the model parameters describe the uncertainty in the parameters and thus describe knowledge uncertainty. Although the distinction between the two is both convenient and important, it is at the same time hypothetical. The division is attributable to the model chosen or developed since modeling assumptions may cause “natural randomness” to become knowledge uncertainties, and vice versa.

This abstract is taken from a paper entitled 'Uncertainty and risk', which was published on December 20, 2004. The paper comprises 3,900 words and 25 references. Individual copies of the paper may be requested by e-mail from the author.