Uncertainty is a term used in subtly different ways in a number of fields, including philosophy, statistics, economics, finance, insurance, psychology, engineering and science. It applies to predictions of future events, to physical measurements already made, or to the unknown unknown. Uncertain EP was the first album of the Irish band The Cranberries. ... A related article is titled uncertainty. ... This article is about the philosophical position. ... Agnosticism (from the Greek a, meaning without, and Gnosticism or gnosis, meaning knowledge) is the philosophical view that the truth value of certain claims—particularly metaphysical claims regarding theology, afterlife or the existence of God, gods, deities, or even ultimate reality—is unknown or, depending on the form of agnosticism... Theory of justification is a part of epistemology that attempts to understand the justification of statements and beliefs. ... Probability is the likelihood that something is the case or will happen. ... It has been suggested that this article or section be merged with estimation. ... This article needs additional references or sources for verification. ... A related article is titled uncertainty. ... Determinism is the philosophical proposition that every event, including human cognition and behavior, decision and action, is causally determined by an unbroken chain of prior occurrences. ... For other uses, see Philosophy (disambiguation). ... This article is about the field of statistics. ... Face-to-face trading interactions on the New York Stock Exchange trading floor. ... Finance studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. ... Insurance, in law and economics, is a form of risk management primarily used to hedge against the risk of a contingent loss. ... Psychology (from Greek: Literally knowledge of the soul (mind)) is both an academic and applied discipline involving the scientific study of mental processes and behavior. ... Engineering is the applied science of acquiring and applying knowledge to design, analysis, and/or construction of works for practical purposes. ... Part of a scientific laboratory at the University of Cologne. ... Measurement is the determination of the size or magnitude of something. ... In decision analysis, an unknown unknown, often shortened to unk-unk, is an uncertainty that is unanticipated and, hence, unaccounted for in a formal decision model. ...

Relation between uncertainty, probability, vagueness and risk

In his seminal work Risk, Uncertainty, and Profit^[1] University of Chicago economist Frank Knight (1921) established the important distinction between risk and uncertainty: The University of Chicago is a private university located principally in the Hyde Park neighborhood of Chicago. ... Frank Hyneman Knight (November 7, 1885 - April 15, 1972) was an important economist in the first half of the twentieth century. ... Lets talk about risk control strategies, anyone with more information and willing to share, please do so. ...

"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 far-reaching 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:^[2] Decision theory is an interdisciplinary area of study, related to and of interest to practitioners in mathematics, statistics, economics, philosophy, management and psychology. ... This article is about the field of statistics. ...

1. 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.
2. 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
3. Risk:A state of uncertainty where some possible outcomes have an undesired effect or significant loss.
4. 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 ^[3]:

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. Image File history File links No higher resolution available. ... Calibrated Probability Assessments are subjective probabilities assigned by individuals who have been trained to assess probabilities in a way that historically represents their uncertainty[1][2]. In other words, when a calibrated person says they are 80% confident in each of 100 predictions they made, they will get about 80...

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 buy insurance for many reasons, then clearly the EOL alone is not the perceived value of avoiding the risk. Insurance, in law and economics, is a form of risk management primarily used to hedge against the risk of a contingent loss. ...

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. Probability theory is the branch of mathematics concerned with analysis of random phenomena. ... 2003 US mortality (life) table, Table 1, Page 1 Actuarial science applies mathematical and statistical methods to finance and insurance, particularly to the assessment of risk. ... Not to be confused with information technology, information science, or informatics. ... Within the context of information theory, self-information is defined as the amount of information that knowledge about (the outcome of) a certain event, adds to someones overall knowledge. ... Not to be confused with information technology, information science, or informatics. ... Cognitive Psychology is the school of psychology that examines internal mental processes such as problem solving, memory, and language. ... expectation in the context of probability theory and statistics, see expected value. ...

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.^[4]:

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 that Heisenberg's uncertainty principle allows. For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... In quantum physics, the Heisenberg uncertainty principle, sometimes called the Heisenberg indeterminacy principle, expresses a limitation on accuracy of (nearly) simultaneous measurement of observables such as the position and the momentum of a particle. ...

Relation between uncertainty, accuracy, precision, standard deviation, standard error, and confidence interval

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. Error bars are used on graphs in the experimental sciences, to indicate the range of one standard deviation on one experimental measurement. ... The International Union of Pure and Applied Chemistry (IUPAC) is an international non-governmental organization devoted to the advancement of chemistry. ... Hydrogen = 1 List of Elements in Atomic Number Order. ... The periodic table of the chemical elements A chemical element, or element, is a type of atom that is defined by its atomic number; that is, by the number of protons in its nucleus. ...

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. In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. ... The standard error of a method of measurement or estimate is the estimated standard deviation of the error in that method. ...

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. Hydrogen = 1 List of Elements in Atomic Number Order. ... The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. ... The standard error of a method of measurement or estimate is the estimated standard deviation of the error in that method. ... In this diagram, the bars represent observation means and the red lines represent the confidence intervals surrounding them. ...

Fields of activities or knowledge where uncertainty is important

• 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 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.

In finance, financial markets facilitate: The raising of capital (in the capital markets); The transfer of risk (in the derivatives markets); and International trade (in the currency markets). ... Rounding to n significant figures is a form of rounding. ... The word error has different meanings in different domains. ... Tug of war is an easily organized, impromptu game that requires little equipment. ... Caravaggio, The Cardsharps, c. ... Chance can be used in any of the following contexts: Probability Luck Randomness See also the Ancient Greek concept of Chance Chance, a 1913 novel by Joseph Conrad. ... For other uses, see Play (disambiguation). ... Scientific modelling is the process of generating abstract or conceptual models. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ... // Meteorology (from Greek: μετέωρον, meteoron, high in the sky; and λόγος, logos, knowledge) is the interdisciplinary scientific study of the atmosphere that focuses on weather processes and forecasting. ... BBCs Alex Deakin presenting a weather report. ... Face-to-face trading interactions on the New York Stock Exchange trading floor. ... Frank Hyneman Knight (November 7, 1885 - April 15, 1972) was an important economist in the first half of the twentieth century. ... Lets talk about risk control strategies, anyone with more information and willing to share, please do so. ... Probability is the likelihood that something is the case or will happen. ... Metrology (from Greek metron (measure), and -logy) is the science of measurement. ... The measurement uncertainty quantifies the distance between the actually measured value of a physical quantity and the true value of the same physical quantity. ... The word error has different meanings in different domains. ... Captain Nemo and Professor Aronnax contemplating measuring instruments in Twenty Thousand Leagues Under the Sea In physics and engineering, measurement is the activity of comparing physical quantities of real-world objects and events. ... As a non-regulatory agency of the United States Department of Commerce’s Technology Administration, the National Institute of Standards (NIST) develops and promotes measurement, standards, and technology to enhance productivity, facilitate trade, and improve the quality of life. ... A random variable can be thought of as the numeric result of operating a non-deterministic mechanism or performing a non-deterministic experiment to generate a random result. ... For Wikipedia statistics, see m:Statistics Statistics is the science and practice of developing human knowledge through the use of empirical data expressed in quantitative form. ... In probability theory and statistics, the variance of a random variable (or somewhat more precisely, of a probability distribution) is a measure of its statistical dispersion, indicating how its possible values are spread around the expected value. ... In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. ...

Uncertainty as an artistic theme

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). The American actor Edwin Booth as Hamlet, seated in a curule chair, c. ... Martin Creed (born 1968) is a British artist noted for his works which hark back to the conceptual art of the 1960s and 1970s. ...

See also

Look up uncertainty in Wiktionary, the free dictionary.

Wikipedia does not have an article with this exact name. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 150 languages. ... The creator of or main contributor to this page may have a conflict of interest with the subject of this article. ... Calibrated Probability Assessments are subjective probabilities assigned by individuals who have been trained to assess probabilities in a way that historically represents their uncertainty[1][2]. In other words, when a calibrated person says they are 80% confident in each of 100 predictions they made, they will get about 80... A related article is titled uncertainty. ... Fuzzy sets are an extension of classical set theory and are used in fuzzy logic. ... Game theory is a branch of applied mathematics that is often used in the context of economics. ... The ASCII codes for the word Wikipedia represented in binary, the numeral system most commonly used for encoding computer information. ... Claude Shannon In information theory, the Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable. ... Not to be confused with information technology, information science, or informatics. ... Wikipedia does not yet have an article with this exact name. ... The measurement uncertainty quantifies the distance between the actually measured value of a physical quantity and the true value of the same physical quantity. ... Morphological analysis (or General Morphological Analysis) is a method developed by Fritz Zwicky (1967, 1969) for exploring all the possible solutions to a multi-dimensional, non-quantified problem complex. ... Probability theory is the branch of mathematics concerned with analysis of random phenomena. ... In statistics, propagation of uncertainty (or propagation of error) is the effect of variables uncertainties (or errors) on the uncertainty of a function based on them. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... “Random” redirects here. ... This article is about the field of statistics. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Ambiguity tolerance is the ability to perceive ambiguity in information and behavior in a neutral and open way. ...

References

A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ...

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 [1]