In the context of risk analysis and decision analysis, uncertainty is usually formulated using probability, although occasionally something like fuzzy arithmetic will be used.

Empirical quantities used as input for risk and decision analysis may have uncertainty arising from many sources. Here are a few, as categorized by M. Granger Morgan and Max Henrion^{1}:

**Random error and statistical variation**– this includes the inherent error in performing physical measurements**Systematic error and subjective judgment**– biases built into observations by the observer**Linguistic imprecision**– when quantities are described using imprecise language**Variability**– items that vary over time or space (e.g., the average number of noders per day this time next year)**Inherent randomness**– for example, wind direction and speed**Disagreement**– conflicting evidence**Approximation**– loss of precision for the sake of simplicity

The importance of this list is that different types of uncertainty need to be recognized and treated in different ways. For example, statistical variation is usually described with a probability distribution. Variability, however, may entail a probability distribution of another probability distribution, which becomes messy quickly.

^{1}Morgan, M. Granger, and Henrion, Max. *Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policay Analysis , Cambridge University Press, 1990.
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