Uncertainty

thumb|Situations often arise wherein a decision must be made when the results of each possible choice are uncertain.

Uncertainty or incertitude refers to situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown, and is particularly relevant for decision-making. Uncertainty arises in partially observable or stochastic or complex or dynamic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, entrepreneurship, finance, medicine, psychology, sociology, engineering, metrology, meteorology, ecology and information science.

Concepts

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, risk, and their measurement as:

The lack of certainty, a state of limited knowledge where it is impossible to exactly describe one or more of the following: the existing state or goal or set of options, the full set of possible future states or their probabilities or their values or utilities to stakeholders, the full set of stakeholders involved, or any other piece of information that inhibits the calculation of the full set of expected values for the options available.

Measurement

Uncertainty, only when considered as objective or subjective risk, can be measured through 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.

Second-order uncertainty

In statistics and economics, second-order uncertainty - expressed as the confidence over outcome probability estimates - is represented in probability density functions over (first-order) probabilities.

Opinions in subjective logic carry this type of uncertainty.

Risk

Risk exists when the future realized point value of a distribution of possible outcomes is not known but an estimated value can be calculated, and where some possible outcomes have an undesired effect or significant loss. Measurement of risk includes a set of outcome probabilities along with the valuations of those outcomes, where some possible outcomes involve losses. This also includes loss functions over continuous variables. Because an expected value for a decision can be calculated, some do not consider risk to be a true type of uncertainty (see below).

Risk versus variability

There is a difference between risk and variability. Risk is quantified by a probability distribution which depends upon knowledge about the likelihood of what the single, true value of the future quantity will be, as in the case of a roll of the dice. Variability is quantified by a distribution of frequencies of multiple instances of the quantity, derived from observed data, as in the case of a batting average.

Knightian uncertainty

In economics, in 1921 Frank Knight distinguished uncertainty from risk with uncertainty being lack of knowledge which is immeasurable and impossible to calculate. To Knight, uncertainty is uninsurable while risk is (hypothetically) insurable. 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 as Knightian uncertainty.

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. Uncertainties have no known expected probability distribution, which can lead to extreme outcomes when borne. Because Knight refers to those who do bear uncertainty as 'entrepreneurs', the field of entrepreneurship includes a stream of research on uncertainty and how it creates opportunities.

Other taxonomies of uncertainties and decisions include more specific characterizations of uncertainty, specifying what is known, knowable, and unknowable about the phenomenon, as well as how it should be approached from an ethics perspective:

thumb|left|550px|A taxonomy of uncertainty

Risk and uncertainty

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 a calibrated probability assessment, the risk 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 terms uncertainty and risk are fairly consistent among 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 used 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 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 on Zadeh's fuzzy logic or subjective logic.

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. Ambiguity can also refer to a type of uncertainty where the range of a distribution of possible outcomes is known, but not their probabilities. Daniel Ellsberg is famous for his urn experiments that illustrated ambiguity, its delineation from risk, and its separate avoidance.

At the subatomic level, 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.

Radical uncertainty

The term 'radical uncertainty' was popularised by John Kay and Mervyn King in their book Radical 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'.

=== In measurements ===

The most commonly used procedure for calculating measurement uncertainty is described in the "Guide to the Expression of Uncertainty in Measurement" (GUM) published by ISO. A derived work is for example the National 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 as random variables, and may be grouped into two categories according to the method used to estimate their numerical values:

Type A, those evaluated by statistical methods
Type B, those 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 metrology, physics, and engineering, the uncertainty or margin of error of a measurement, when explicitly stated, is given by a range of values likely to enclose the true value. The uncertainty is often the standard uncertainty, which assumes an approximately Gaussian distribution, with the uncertainty expressing one standard deviation. This may be denoted by error bars on a graph, or by the following notations:

measured value ± uncertainty
measured value
measured value (uncertainty)

In the last notation, parentheses are the concise notation for the ± notation. For example, applying 10 meters in a scientific or engineering application, it could be written or , by convention meaning accurate to within 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 is understood that 10.5 means , and 10.50 means , also written and respectively. But if the accuracy is within two tenths, the uncertainty is ± one tenth, and it is required to be explicit: and or and . The numbers in parentheses apply to the numeral left of themselves, and are not part of that number, but part of a notation of uncertainty. They apply to the least significant digits. For instance, stands for , while stands for . 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.

"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." 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. 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). One way that journalists inflate uncertainty is by describing new research that contradicts past research without providing context for the change. 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.

In physics, the Heisenberg uncertainty principle forms the basis of modern quantum mechanics.
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).
Uncertainty is 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). Knightian uncertainty involves a situation that has unknown probabilities. resulting in the Hellenistic philosophies of Pyrrhonism and Academic Skepticism, the first schools of philosophical skepticism. Aporia and acatalepsy represent key concepts in ancient Greek philosophy regarding uncertainty.

William MacAskill, a philosopher at Oxford University, has also discussed the concept of Moral Uncertainty. 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."

Artificial intelligence

References

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)
Understanding Uncertainty site from Cambridge's Winton programme

Uncertainty

Concepts

Uncertainty

Measurement

Second-order uncertainty

Risk

Risk versus variability

Knightian uncertainty

Risk and uncertainty

Radical uncertainty

Artificial intelligence

See also

References

Further reading

External links