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Uncertainty orincertitude refers to situations involving imperfect or unknowninformation. It applies to predictions of future events, to physical measurements that are already made, or to the unknown, and is particularly relevant fordecision-making. Uncertainty arises inpartially observable orstochastic environments, as well as due toignorance,indolence, or both.[1] It arises in any number of fields, includinginsurance,philosophy,physics,statistics,economics, finance,medicine,psychology,sociology,engineering,metrology,meteorology,ecology andinformation science.
Although the terms are used in various ways among the general public, many specialists indecision theory,statistics and other quantitative fields have defined uncertainty, risk, and their measurement as:
The lack ofcertainty, a state of limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome.[2]
Uncertainty can be measured through a set of possible states or outcomes whereprobabilities are assigned to each possible state or outcome – this also includes the application of aprobability density function to continuous variables.[3]
In statistics and economics, second-order uncertainty is represented in probability density functions over (first-order) probabilities.[4][5]
Opinions insubjective logic[6] carry this type of uncertainty.
Risk is a state of uncertainty, where some possible outcomes have an undesired effect or significant loss. Measurement of risk includes 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.[7][8][9][10]
There is a difference between uncertainty and variability. Uncertainty is quantified by a probability distribution which depends upon knowledge about the likelihood of what the single, true value of the uncertain quantity is. Variability is quantified by a distribution of frequencies of multiple instances of the quantity, derived from observed data.[11]
In economics, in 1921Frank Knight distinguished uncertainty from risk with uncertainty being lack of knowledge which is immeasurable and impossible to calculate. Because of the absence of clearly defined statistics in most economic decisions where people face uncertainty, he believed that we cannot measure probabilities in such cases; this is now referred to asKnightian uncertainty.[12]
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.
There is a fundamental distinction between the reward for taking a known risk and that for assuming a risk whose value itself is not known. It is so fundamental, indeed, that … a known risk will not lead to any reward or special payment at all.
— Frank Knight
Knight pointed out that the unfavorable outcome of known risks can be insured during the decision-making process because it has a clearly defined expected probability distribution. Unknown risks have no known expected probability distribution, which can lead to extremely risky company decisions.
Other taxonomies of uncertainties and decisions include a broader sense of uncertainty and how it should be approached from an ethics perspective:[14]
There are some things that you know to be true, and others that you know to be false; yet, despite this extensive knowledge that you have, there remain many things whose truth or falsity is not known to you. We say that you are uncertain about them. You are uncertain, to varying degrees, about everything in the future; much of the past is hidden from you; and there is a lot of the present about which you do not have full information. Uncertainty is everywhere and you cannot escape from it.
For example, if it is unknown whether or not it will rain tomorrow, then there is a state of uncertainty. If probabilities are applied to the possible outcomes using weather forecasts or even just acalibrated probability assessment, the uncertainty has been quantified. Suppose it is quantified as a 90% chance of sunshine. If there is a major, costly, outdoor event planned for tomorrow then there is a risk since there is a 10% chance of rain, and rain would be undesirable. Furthermore, if this is a business event and $100,000 would be lost if it rains, then the risk has been quantified (a 10% chance of losing $100,000). These situations 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% × $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 onto 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 termsuncertainty andrisk are fairly consistent among fields such asprobability theory,actuarial science, andinformation theory. Some also create new terms without substantially changing the definitions of uncertainty or risk. For example,surprisal is a variation on uncertainty sometimes used ininformation theory. But outside of the more mathematical uses of the term, usage may vary widely. Incognitive psychology, uncertainty can be real, or just a matter of perception, such asexpectations, threats, etc.
Vagueness is a form of uncertainty where the analyst is unable to clearly differentiate between two different classes, such as 'person of average height' and 'tall person'. This form of vagueness can be modelled by some variation onZadeh'sfuzzy logic orsubjective logic.[15]
Ambiguity is a form of uncertainty where even the possible outcomes have unclear meanings and interpretations. The statement"He returns from the bank" is ambiguous because its interpretation depends on whether the word 'bank' is meant as"the side of a river" or"a financial institution". Ambiguity typically arises in situations where multiple analysts or observers have different interpretations of the same statements.[16]
At the subatomic level, uncertainty may be a fundamental and unavoidable property of the universe. Inquantum mechanics, theHeisenberg 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.[17]
The term 'radical uncertainty' was popularised byJohn Kay andMervyn King in their bookRadical Uncertainty: Decision-Making for an Unknowable Future, published in March 2020. It is distinct from Knightian uncertainty, by whether or not it is 'resolvable'. If uncertainty arises from a lack of knowledge, and that lack of knowledge is resolvable by acquiring knowledge (such as by primary or secondary research) then it is not radical uncertainty. Only when there are no means available to acquire the knowledge which would resolve the uncertainty, is it considered 'radical'.[18][19]
The most commonly used procedure for calculating measurement uncertainty is described in the "Guide to the Expression of Uncertainty in Measurement" (GUM) published byISO. A derived work is for example theNational Institute of Standards and Technology (NIST) Technical Note 1297, "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results", and the Eurachem/Citac publication "Quantifying Uncertainty in Analytical Measurement". The uncertainty of the result of a measurement generally consists of several components. The components are regarded asrandom variables, and may be grouped into two categories according to the method used to estimate their numerical values:
By propagating thevariances 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 thestandard deviation of a repeated observation.
Inmetrology,physics, andengineering, the uncertainty ormargin of error of a measurement, when explicitly stated, is given by a range of values likely to enclose the true value. This may be denoted byerror bars on a graph, or by the following notations:[citation needed]
In the last notation, parentheses are the concise notation for the ± notation. For example, applying 101⁄2 meters in a scientific or engineering application, it could be written10.5 m or10.50 m, by convention meaning accurate towithin one tenth of a meter, or one hundredth. The precision is symmetric around the last digit. In this case it's half a tenth up and half a tenth down, so 10.5 means between 10.45 and 10.55. Thus it isunderstood that 10.5 means10.5±0.05, and 10.50 means10.50±0.005, also written10.50(5) and10.500(5) respectively. But if the accuracy is within two tenths, the uncertainty is ± one tenth, and it isrequired to be explicit:10.5±0.1 and10.50±0.01 or10.5(1) and10.50(1). The numbers in parenthesesapply to the numeral left of themselves, and are not part of that number, but part of a notation of uncertainty. They apply to theleast significant digits. For instance,1.00794(7) stands for1.00794±0.00007, while1.00794(72) stands for1.00794±0.00072.[20] This concise notation is used for example byIUPAC in stating theatomic mass ofelements.
The middle notation is used when the error is not symmetrical about the value – for example3.4+0.3
−0.2. This can occur when using a logarithmic scale, for example.
Uncertainty of a measurement can be determined by repeating a measurement to arrive at an 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 thestandard error of the mean, which is the standard deviation divided by the square root of the number of measurements. This procedure neglectssystematic errors, however.[citation needed]
When the uncertainty represents the standard error of the measurement, then about 68.3% of the time, the true value of the measured quantity falls within the stated uncertainty range. For example, it is likely that for 31.7% of the atomic mass values given on thelist 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 thenormal distribution, and they apply only if the measurement process produces normally distributed errors. In that case, the quotedstandard errors are easily converted to 68.3% ("onesigma"), 95.4% ("two sigma"), or 99.7% ("three sigma")confidence intervals.[citation needed]
In this context, uncertainty depends on both theaccuracy and precision of the measurement instrument. The lower the accuracy and precision of an instrument, the larger the measurement uncertainty is. Precision is often determined as the standard deviation of the repeated measures of a given value, namely using the same method described above to assess measurement uncertainty. However, this method is correct only when the instrument is accurate. When it is inaccurate, the uncertainty is larger than the standard deviation of the repeated measures, and it appears evident that the uncertainty does not depend only on instrumental precision.
Uncertainty in science, and science in general, may be interpreted differently in the public sphere than in the scientific community.[21] This is due in part to the diversity of the public audience, and the tendency for scientists to misunderstand lay audiences and therefore not communicate ideas clearly and effectively.[21] One example is explained by theinformation deficit model. Also, in the public realm, there are often many scientific voices giving input on a single topic.[21] For example, depending on how an issue is reported in the public sphere, discrepancies between outcomes of multiple scientific studies due to methodological differences could be interpreted by the public as a lack of consensus in a situation where a consensus does in fact exist.[21] This interpretation may have even been intentionally promoted, as scientific uncertainty may be managed to reach certain goals. For example,climate change deniers took the advice ofFrank Luntz to frameglobal warming as an issue of scientific uncertainty, which was a precursor to the conflict frame used by journalists when reporting the issue.[22]
"Indeterminacy can be loosely said to apply to situations in which not all the parameters of the system and their interactions are fully known, whereas ignorance refers to situations in which it is not known what is not known."[23] These unknowns, indeterminacy and ignorance, that exist in science are often "transformed" into uncertainty when reported to the public in order to make issues more manageable, since scientific indeterminacy and ignorance are difficult concepts for scientists to convey without losing credibility.[21] Conversely, uncertainty is often interpreted by the public as ignorance.[24] The transformation of indeterminacy and ignorance into uncertainty may be related to the public's misinterpretation of uncertainty as ignorance.
Journalists may inflate uncertainty (making the science seem more uncertain than it really is) or downplay uncertainty (making the science seem more certain than it really is).[25] One way that journalists inflate uncertainty is by describing new research that contradicts past research without providing context for the change.[25] Journalists may give scientists with minority views equal weight as scientists with majority views, without adequately describing or explaining the state ofscientific consensus on the issue.[25] In the same vein, journalists may give non-scientists the same amount of attention and importance as scientists.[25]
Journalists may downplay uncertainty by eliminating "scientists' carefully chosen tentative wording, and by losing these caveats the information is skewed and presented as more certain and conclusive than it really is".[25] Also, stories with a single source or without any context of previous research mean that the subject at hand is presented as more definitive and certain than it is in reality.[25] There is often a "product over process" approach toscience journalism that aids, too, in the downplaying of uncertainty.[25] Finally, and most notably for this investigation, when science is framed by journalists as a triumphant quest, uncertainty is erroneously framed as "reducible and resolvable".[25]
Some media routines and organizational factors affect the overstatement of uncertainty; other media routines and organizational factors help inflate the certainty of an issue. Because the general public (in the United States) generally trusts scientists, when science stories are covered without alarm-raising cues from special interest organizations (religious groups, environmental organizations, political factions, etc.) they are often covered in a business related sense, in an economic-development frame or a social progress frame.[26] The nature of these frames is to downplay or eliminate uncertainty, so when economic and scientific promise are focused on early in the issue cycle, as has happened with coverage of plant biotechnology and nanotechnology in the United States, the matter in question seems more definitive and certain.[26]
Sometimes, stockholders, owners, or advertising will pressure a media organization to promote the business aspects of a scientific issue, and therefore any uncertainty claims which may compromise the business interests are downplayed or eliminated.[25]
InWestern philosophy the first philosopher to embrace uncertainty wasPyrrho[29] resulting in theHellenistic philosophies ofPyrrhonism andAcademic Skepticism, the first schools ofphilosophical skepticism.Aporia andacatalepsy represent key concepts in ancient Greek philosophy regarding uncertainty.
William MacAskill, a philosopher at Oxford University, has also discussed the concept of Moral Uncertainty.[30] Moral Uncertainty is "uncertainty about how to act given lack of certainty in any one moral theory, as well as the study of how we ought to act given this uncertainty."[31]
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