Dictionary Definition
uncertainty
Noun
1 being unsettled or in doubt; "the uncertainty
of the outcome" [syn: uncertainness] [ant:
certainty]
2 the state of being unsure of something [syn:
doubt, incertitude, dubiety, doubtfulness, dubiousness] [ant: certainty]
User Contributed Dictionary
English
Etymology
Pronunciation
Noun
uncertainty (plural uncertainties) doubt; the condition of being uncertain or without conviction.
 Something uncertain or ambiguous.
 (mathematics) A parameter that measures the dispersion of a range of measured values.
Antonyms
Translations
doubt; the condition of being uncertain
 Czech: nejistota
 German: Unsicherheit
 Polish: niepewność
 Russian: неуверенность (n'euv'ér'ennost’) , сомнение (somn'énije)
Something uncertain or ambiguous
 German: Unsicherheit
 Russian: неуверенность (n'euv'ér'ennost’) , неясность (n'ejásnist') , неопределённость (n'eopr'ed'el'ónnost')
(mathematics) A parameter that measures the
dispersion
 Russian: погрешность (pogr'éšnost') , неточность (n'etóčnost'), неопределённость (n'eopr'ed'el'ónnost')
 ttbc Dutch: onzekerheid
 ttbc Spanish: incertidumbre
Extensive Definition
Uncertainty is a term used in subtly different
ways in a number of fields, including philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information
science. It applies to predictions of future events, to
physical measurements already made,
or to the unknown.
Concepts
In his seminal work Risk, Uncertainty, and Profit
University
of Chicago economist Frank Knight
(1921) established the important distinction between risk and uncertainty:
 "Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are farreaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.... It will appear that a measurable uncertainty, or 'risk' proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all."
Although the terms are used in various ways among
the general public, many specialists in decision
theory, statistics and other
quantitative fields have defined uncertainty and risk more
specifically. Doug Hubbard defines uncertainty and risk as:

 Uncertainty: The lack of certainty, A state of having limited knowledge where it is impossible to exactly describe existing state or future outcome, more than one possible outcome.
 Measurement of Uncertainty:A set of possible states or outcomes where probabilities are assigned to each possible state or outcome  this also includes the application of a probability density function to continuous variables
 Risk:A state of uncertainty where some possible outcomes have an undesired effect or significant loss.
 Measurement of Risk:A set of measured uncertainties where some possible outcomes are losses, and the magnitudes of those losses  this also includes loss functions over continuous variables.
There are other different taxonomy of
uncertainties and decisions that include a more broad sense of
uncertainty and how it should be approached from an ethics
perspective :
For example, if you do not know whether it will
rain tomorrow, then you have a state of uncertainty. If you apply
probabilities to the possible outcomes using weather forecasts or
even just a
calibrated probability assessment, you have quantified the
uncertainty. Suppose you quantify your uncertainty as a 90% chance
of sunshine. If you are planning a major, costly, outdoor event for
tomorrow then you have risk since there is a 10% chance of rain and
rain would be undesirable. Furthermore, if this is a business event
and you would lose $100,000 if it rains, then you have quantified
the risk (a 10% chance of losing $100,000). These situation can be
made even more realistic by quantifying light rain vs. heavy rain,
the cost of delays vs. outright cancellation, etc.
Some may represent the risk in this example as
the "expected opportunity loss" (EOL) or the chance of the loss
multiplied by the amount of the loss (10% x $100,000 = $10,000).
That is useful if the organizer of the event is "risk neutral"
which most people are not. Most would be willing to pay a premium
to avoid the loss. An insurance company, for
example, would compute an EOL as a minimum for any insurance
coverage, then add on to that other operating costs and profit.
Since many people are willing to buy insurance for many reasons,
then clearly the EOL alone is not the perceived value of avoiding
the risk.
Quantitative uses of the terms uncertainty and
risk are fairly consistent from fields such as probability
theory, actuarial
science, and information
theory. Some also create new terms without substantially
changing the definitions of uncertainty or risk. For example,
surprisal is a
variation on uncertainty sometimes uses in information
theory. But outside of the more mathematical uses of the term,
usage may vary widely. In cognitive
psychology, uncertainty can be real, or just a matter of
perception, such as expectations, threats,
etc.
Vagueness or ambiguity are sometimes described as
"second order uncertainty", where there is uncertainty even about
the definitions of uncertain states or outcomes. The difference
here is that this uncertainty is about the human definitions and
concepts not an objective fact of nature. It has been argued that
ambiguity, however, is always avoidable while uncertainty (of the
"first order" kind) is not necessarily avoidable.:
Uncertainty may be purely a consequence of a lack
of knowledge of obtainable facts. That is, you may be uncertain
about whether a new rocket design will work, but this uncertainty
can be removed with further analysis and experimentation. At the
subatomic level, however, uncertainty may be a fundamental and
unavoidable property of the universe. In quantum
mechanics, the
Heisenberg Uncertainty Principle puts limits on how much an
observer can ever know about the position and velocity of a
particle. This may not just be ignorance of potentially obtainable
facts but that there is no fact to be found. There is some
controversy in physics as to whether such uncertainty is an
irreducible property of nature or if there are "hidden variables"
that would describe the state of a particle even more exactly than
Heisenberg's uncertainty principle allows.
Measures
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, then the mean measurement value has a much smaller
uncertainty, equal to the
standard error of the mean, 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.
Applications
 Investing in financial markets such as the stock market.
 Uncertainty is used in engineering notation when talking about significant figures. Or the possible error involved in measuring things such as distance.
 Uncertainty is designed into games, most notably in gambling, where chance is central to play.
 In scientific modelling, in which the prediction of future events should be understood to have a range of expected values.
 In physics in certain situations, uncertainty has been elevated into a principle, the uncertainty principle.
 In weather forecasting 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 risk assessment and risk management.
 In metrology, measurement uncertainty is a central concept quantifying the dispersion one may reasonably attribute to a measurement result. Such an uncertainty can also be referred to as a measurement error. 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" and the Eurachem/Citac publication "Uncertatinty in measurements" (available at the Eurachem homepage). 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:

 Type A, those which are evaluated by statistical methods,
 Type B, 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.
 Uncertainty has been a common theme in art, both as a thematic device (see, for example, the indecision of Hamlet), and as a quandary for the artist (such as Martin Creed's difficulty with deciding what artworks to make).
See also
 Applied Information Economics
 calibrated probability assessment
 Certainty
 Fuzzy set theory
 Game theory
 Information
 Information entropy
 Information theory
 Inquiry
 Measurement uncertainty
 Morphological analysis (problemsolving)
 Probability theory
 Propagation of uncertainty
 Quantum mechanics
 Randomness
 Statistics
 Statistical mechanics
 Uncertainty tolerance
References
Further reading
 Understanding Uncertainty
 Reasoning about Uncertainty
External links
 Measurement Uncertainties in Science and Technology, Springer 2005
 Proposal for a New Error Calculus
 Estimation of Measurement Uncertainties — an Alternative to the ISO Guide
 Bibliography of Papers Regarding Measurement Uncertainty
 Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results
 Strategic Engineering: Designing Systems and Products under Uncertainty (MIT Research Group)
 Research results regarding uncertainty models, uncertainty quantification, and uncertainty processing
 Decision tree to choose an uncertainty method for hydrological and hydraulic modelling, Choosing an uncertainty analysis for flood modelling.
 Decision Analysis in Health Care George Mason University online course offering lectures and tools for modeling and mitigating uncertainty in health care scenarios.
 Uri Weiss, The Regressive Effect of Legal Uncertainty http://law.bepress.com/cgi/viewcontent.cgi?article=1030&context=taulwps
 NUSAP.net educational website dedicated to coping with uncertainty and quality in science for policy, for all actors involved in the science policy interface.
uncertainty in German: Unsicherheit
uncertainty in Spanish: Incertidumbre
uncertainty in Estonian: Määramatus
uncertainty in Finnish: Virhe
uncertainty in Japanese: 不確かさ
uncertainty in Polish: Niepewność
uncertainty in Slovenian: negotovost
uncertainty in Swedish: Osäkerhet
uncertainty in Chinese: 不确定性
Synonyms, Antonyms and Related Words
Pyrrhonism, accidentality, actuarial
calculation, adventitiousness,
agitation, ambiguity, ambiguousness, ambitendency, ambivalence, amphibology, anxiety, apprehension, arrhythmia, bleariness, blur, blurriness, bother, break, brokenness, calculated risk,
capriciousness,
casualness, chance, chanciness, change of mind,
changeableness,
choppiness,
cliffhanging, complexity of meaning, concern, criticalness, darkness, defocus, delicacy, destiny, desultoriness, deviability, diffidence, dimness, disconnectedness,
discontinuity,
disquiet, distress, distrust, distrustfulness, double
entendre, double meaning, double reference, doublemindedness,
doubt, doubtfulness, dread, dubiety, dubiousness, eccentricity, equivocacy, equivocality, equivocalness, erraticism, erraticness, expectant
waiting, faintness,
fate, feebleness, fencesitting,
fencestraddling, fibrillation, fickleness, filminess, fitfulness, fits and starts,
flier, flightiness, fluctuation, flukiness, fogginess, fortuitousness, fortuity, fortune, freakishness, fuzziness, gamble, good fortune, good luck,
halfbelief, halfvisibility, hap, happenstance, happy chance,
hazard, hazardousness, haziness, heedless hap,
hesitation, how they
fall, impulsiveness, incertitude, inconsistency, inconstancy, indecision, indecisiveness, indefiniteness, indeterminacy, indeterminateness,
indistinctness,
indistinguishability,
infirmity of purpose, insecurity, instability, intermittence, irony, irregularity, irresolution, jerkiness, law of averages,
leeriness, levels of
meaning, lot, low profile,
luck, mercuriality, misdoubt, misgiving, mistiness, mistrust, mistrustfulness,
moira, moodiness, mugwumpery, mugwumpism, multivocality, opportunity, paleness, paronomasia, patchiness, perilousness, perturbation, pessimism, play, plunge, polysemousness, polysemy, precariousness, principle
of indeterminacy, probability, problematicness,
punning, query, question, random sample,
reserve, restlessness, richness of
meaning, risk, riskiness, roughness, run of luck,
salt, scruple, scrupulousness, second
thoughts, selfdoubt, semivisibility, serendipity, shadow of
doubt, shadowiness,
shakiness, shiftiness, skepticalness, skepticism, slipperiness, soft focus,
spasticity, speculation, sporadicity, sporadicness, spottiness, stagger, statistical
probability, suspense,
suspicion, suspiciousness, sword of
Damocles, tergiversation, the
breaks, theory of probability, ticklish business, ticklishness, total
skepticism, totteriness, touchiness, trouble, uncertainty principle,
unclearness,
undecidedness,
undependability,
undeterminedness,
uneasiness, unevenness, unfixedness, unhealthiness, unmethodicalness,
unplainness,
unpredictability,
unreliability,
unsafeness, unsettledness, unsettlement, unsoundness, unstableness, unsteadfastness,
unsteadiness,
unsureness, unsystematicness,
untrustworthiness,
vague appearance, vagueness, variability, variation, variety, venture, waiting, wantonness, wariness, waywardness, weakness, whatever comes,
whimsicality,
wobble, wonder, worry