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That is, the probability function f(x) lies between zero and one for every value of x in the sample space Ω, and the sum of f(x) over all values x in the sample space Ω is equal to 1. An event is defined as any subset of the sample space . The probability of the event is defined as
The certainty effect is the psychological effect resulting from the reduction of probability from certain to probable (Tversky & Kahneman 1986). It is an idea introduced in prospect theory .
The observer is not allowed to say "I do not know", or "I am not sure", or "I did not see anything". In that sense the observer's choice is forced between the two alternatives. Both options can be presented concurrently (as in the above example) or sequentially in two intervals (also known as two-interval forced choice, 2IFC). For example, to ...
An individual that is risk averse has a certainty equivalent that is smaller than the prediction of uncertain gains. The risk premium is the difference between the expected value and the certainty equivalent. For risk-averse individuals, risk premium is positive, for risk-neutral persons it is zero, and for risk-loving individuals their risk ...
Most theoretical analyses of risky choices depict each option as a gamble that can yield various outcomes with different probabilities. [2] Widely accepted risk-aversion theories, including Expected Utility Theory (EUT) and Prospect Theory (PT), arrive at risk aversion only indirectly, as a side effect of how outcomes are valued or how probabilities are judged. [3]
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. [1] An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one.
Uncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known.
Words of estimative probability (WEP or WEPs) are terms used by intelligence analysts in the production of analytic reports to convey the likelihood of a future event occurring. A well-chosen WEP gives a decision maker a clear and unambiguous estimate upon which to base a decision.