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. A related article is titled Uncertainty. For statistical certainty see Probability. Nihilism (from the Latin nihil, nothing is a philosophical position that argues that Existence is without objective meaning Purpose Agnosticism ( Greek: α- a-, without + γνώσις gnōsis, knowledge after Gnosticism) is the philosophical view that the Probability is the likelihood or chance that something is the case or will happen An approximation (represented by the symbol ≈ is an inexact representation of something that is still close enough to be useful Belief is the psychological state in which an individual holds a Proposition or Premise to be true Epistemology (from Greek επιστήμη - episteme, "knowledge" + λόγος, " Logos " or theory of knowledge A related article is titled Uncertainty. For statistical certainty see Probability. Determinism is the philosophical Proposition that every event including human cognition and behaviour decision and action is causally determined Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. Economics is the social science that studies the production distribution, and consumption of goods and services. The field of finance refers to the concepts of Time, Money and Risk and how they are interrelated 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 grc ψῡχή psȳkhē, "breath life soul" and grc -λογία -logia) is an Academic and Sociology (from Latin: socius "companion" and the suffix -ology "the study of" from Greek λόγος lógos "knowledge" Engineering is the Discipline and Profession of applying technical and scientific Knowledge and Information science is an interdisciplinary science primarily concerned with the collection classification, manipulation storage retrieval and dissemination It applies to predictions of future events, to physical measurements already made, or to the unknown. Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as

Concepts

In his seminal work Risk, Uncertainty, and Profit^[1] 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 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 of the twentieth century Risk is a Concept that denotes the precise probability of specific eventualities . . . 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. Decision theory in Mathematics and Statistics is concerned with identifying the Values uncertainties and other issues relevant in a given Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. Doug Hubbard defines uncertainty and risk as:^[2]

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. Calibrated probability assessments are subjective probabilities assigned by individuals who have been trained to assess probabilities in a way that historically represents their 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. Insurance, in Law and Economics, is a form of Risk management primarily used to hedge against the Risk of a contingent loss 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. Probability theory is the branch of Mathematics concerned with analysis of random phenomena Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the Insurance and Finance Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information. 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. In Information theory (elaborated by Claude E Shannon, 1948) self-information is a measure of the information content associated with the outcome Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information. 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. Cognitive psychology is a branch of Psychology that investigates internal mental processes such as problem solving memory and language In the case of Uncertainty, expectation is what is considered the most likely to happen

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. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In Quantum physics, the Heisenberg uncertainty principle states that locating a particle in a small region of space makes the Momentum of the particle uncertain 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). Error bars are used on graphs to indicate the error in a reported measurement The latter "concise notation" is used for example by IUPAC in stating the atomic mass of elements. The International Union of Pure and Applied Chemistry ( IUPAC) (aɪjuːpæk or ay-yoo-pec) is an international Non-governmental organization A chemical element is a type of Atom that is distinguished by its Atomic number; that is by the number of Protons in its nucleus. 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. In Probability and Statistics, the standard deviation is a measure of the dispersion of a collection of 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. The standard error of a method of measurement or estimation 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. The normal distribution, also called the Gaussian distribution, is an important family of Continuous probability distributions applicable in many fields In that case, the quoted standard errors are easily converted to 68. The standard error of a method of measurement or estimation is the estimated Standard deviation of the error in that method 2% ("one sigma"), 95. 4% ("two sigma"), or 99. 7% ("three sigma") confidence intervals. In Statistics, a confidence interval (CI is an interval estimate of a Population parameter.

Applications

• Investing in financial markets such as the stock market. In Economics, a financial market is a mechanism that allows people to easily buy and sell ( Trade) financial Securities (such as stocks and bonds
• Uncertainty is used in engineering notation when talking about significant figures. The significant figures (also called significant digits and abbreviated sig figs) of a number are those digits that carry meaning contributing to its accuracy Or the possible error involved in measuring things such as distance. The word error has different meanings and usages relative to how it is conceptually applied
• Uncertainty is designed into games, most notably in gambling, where chance is central to play. A game is a structured activity, usually undertaken for Enjoyment and sometimes also used as an Educational tool
• In scientific modelling, in which the prediction of future events should be understood to have a range of expected values. Scientific modelling is the process of generating abstract, conceptual, Graphical and or mathematical models.
• In physics in certain situations, uncertainty has been elevated into a principle, the uncertainty principle. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Quantum physics, the Heisenberg uncertainty principle states that locating a particle in a small region of space makes the Momentum of the particle uncertain
• In weather forecasting it is now commonplace to include data on the degree of uncertainty in a weather forecast. Meteorology (from Greek grc μετέωρος metéōros, "high in the sky" and grc -λογία -logia) is the Interdisciplinary Weather forecasting is the application of science and technology to predict the state of the atmosphere for a future time and a given location
• Uncertainty is often an important factor in economics. Economics is the social science that studies the production distribution, and consumption of goods and services. 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). Frank Hyneman Knight ( November 7, 1885 - April 15, 1972) was an important Economist of the twentieth century Risk is a Concept that denotes the precise probability of specific eventualities Probability is the likelihood or chance that something is the case or will happen 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. Risk assessment is a common first step in a Risk management process For non-business risks see Risk or the disambiguation page Risk analysis. ^[5]
• In metrology, measurement uncertainty is a central concept quantifying the dispersion one may reasonably attribute to a measurement result. Metrology (from Ancient Greek metron (measure and logos (study of is the Science of Measurement. In Metrology, measurement uncertainty describes a region about an observed value of a Physical quantity which is likely to enclose the true value of that quantity Such an uncertainty can also be referred to as a measurement error. The word error has different meanings and usages relative to how it is conceptually applied 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. In the Physical sciences Quality assurance, and Engineering, Measurement is the activity of obtaining and comparing physical quantities

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. A random variable is a rigorously defined mathematical entity used mainly to describe Chance and Probability in a mathematical way Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. 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. In Probability theory and Statistics, the variance of a Random variable, Probability distribution, or sample is one measure of The simplest form is the standard deviation of a repeated observation. In Probability and Statistics, the standard deviation is a measure of the dispersion of a collection of values

• 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). Hamlet is a Tragedy by William Shakespeare, believed to have been written between 1599 and 1601 Martin Creed (born 1968 is an English Artist noted for his works which are grounded in the Conceptual art of the 1960s and 1970s

See also

References

Further reading

• Lindley, Dennis V. (2006-09-11). Dennis Victor Lindley (born July 25, 1923) is a British statistician, decision theorist and leading advocate of Bayesian statistics. Understanding Uncertainty. Wiley-Interscience. John Wiley & Sons Inc, also referred to as Wiley, is a global Publishing company that markets its products to professionals and consumers students and instructors ISBN 978-0470043837.  
• Halpern, Joseph (2005-09-01). Joseph Yehuda Halpern is a professor of Computer science at Cornell University. Reasoning about Uncertainty. MIT Press. The MIT Press is a University press affiliated with the Massachusetts Institute of Technology (MIT in Cambridge Massachusetts ( USA) ISBN 978-0262582599.  

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]
• NUSAP.net educational website dedicated to coping with uncertainty and quality in science for policy, for all actors involved in the science policy interface.