Uncertainty

State of having limited knowledge where it is impossible to exactly describe an existing state or future outcome, or more than one possible outcome. The variables describing the complexity are not known, and it is therefore not even possible for us to attach possibilities to them. (1) It is a term used in a number of fields, including philosophy, statistics, economics, finance, insurance, psychology, and science. It applies to predictions of future events, to physical measurements already made, or to the unknown. In his seminal work Risk, Uncertainty, and Profit, Frank Knight (1921) established the important distinction between risk and uncertainty: Risk is defined as uncertainty based on a well grounded (quantitative) probability. Formally, Risk = (the probability that some event will occur) X (the consequences if it does occur). Genuine uncertainty, on the other hand, cannot be assigned such a (well grounded) probability. Furthermore, genuine uncertainty can often not be reduced significantly by attempting to gain more information about the phenomena in question and their causes. There are other measures of uncertainty In stochastics, risk is an uncertainty for 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. Mathematicians handle uncertainty using probability theory, Dempster-Shafer theory, fuzzy logic. Surprisal is a measure of uncertainty in information theory. The uncertainty of a measurement is stated by giving a range of values which are likely to enclose the true value. This may be denoted by error bars on a graph, or as value ± uncertainty, or as decimal fraction(uncertainty). The latter "concise notation" is used for example by IUPAC in stating the atomic mass of elements. There, 1.00794(7) stands for 1.00794 ± 0.00007. Often, the uncertainty of a measurement is found by repeating the measurement enough times to get a good estimate of the standard deviation of the values. Then, any single value has an uncertainty equal to the standard deviation. However, if the values are averaged and the mean is reported, then the averaged measurement has uncertainty equal to the standard error which is the standard deviation divided by the square root of the number of measurements. When the uncertainty represents the standard error of the measurement, then about 68.2% of the time, the true value of the measured quantity falls within the stated uncertainty range. For example, it is likely that for 31.8% of the atomic mass values given on the list of elements by atomic mass, the true value lies outside of the stated range. If the width of the interval is doubled, then probably only 4.6% of the true values lie outside the doubled interval, and if the width is tripled, probably only 0.3% lie outside. These values follow from the properties of the normal distribution, and they apply only if the measurement process produces normally distributed errors. In that case, the quoted standard errors are easily converted to 68.2% ("one sigma"), 95.4% ("two sigma"), or 99.7% ("three sigma") confidence intervals.