Uncertainty is an inevitable part of the assertion of knowledge, see Bayesian probability.

Relation between uncertainty, probability and risk

Mathematicians handle uncertainty using probability theory, Dempster-Shafer theory, fuzzy logic. See also probability.

There is a distinction between uncertainty and risk.

• In stochastics, risk is an uncertainty which probability can be calculated (with past statistics for example) or at least estimated (doing projection scenarios) mathematically.
• In insurance, risk deals only with negative uncertainty (those bringing loss or harm)

In cognitive psychology, uncertainty can be real, or just a matter of perception, such as expectations, threats, etc.

Fields of activities or knowledge where uncertainty is important

• Investing in financial markets such as the stock market.

• Uncertainty is designed into games, most notably in gambling, where chance is central to play.

• In physics in certain situations, uncertainty has been elevated into a principle, the uncertainty principle.

• In weather forcasting it is now commonplace to include data on the degree of uncertainty in a weather forecast.

• Uncertainty is often an important factor in economics. According to economist Frank Knight, it is different from risk, where there is a specific probability assigned to each outcome (as when flipping a fair coin). Uncertainty involves a situation that has unknown probabilities, while the estimated probabilities of possible outcomes need not add to unity.

• In metrology, measurement uncertainty is a central concept quantifying the dispersion one may reasonably attribute to a measurement result. In daily life, measurement uncertainty is often implicit ("He is 6 feet tall" give or take a few inches), while for any serious use an explicit statement of the measurement uncertainty is necessary. The expected measurement uncertainty of many measuring instruments (scales, oscilloscopes, force gages, rulers, thermometers, etc) is often stated in the manufacturers specification.

The most commonly used procedure for calculating measurement uncertainty is described in the Guide to the Expression of Uncertainty in Measurement (often referred to as "the GUM") published by ISO. A derived work is for example the National Institute for Standards and Technology (NIST) publication NIST Technical Note 1297 "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results". The uncertainty of the result of a measurement generally consists of several components. The components are regarded as random variables, and may be grouped into two categories according to the method used to estimate their numerical values:

• 1. those which are evaluated by statistical methods,
  2. those which are evaluated by other means, e.g. by assigning a probability distribution.

By propagating the variances of the components through a function relating the components to the measurement result, the combined measurement uncertainty is given as the square root of the resulting variance. The simplest form is the standard deviation of a repeated observation.

Further reading

• New York Times article, "Studies Suggest Unknown Form of Matter Exists" by Ames Glanz, July 31, 2002
• Bibliography of Papers Regarding Measurement Uncertainty
• Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results