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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.
Certainty condition: The median price paid to avoid an electric shock was $19.86. Most participants (24/30) preferred receiving the shock over paying more than $20. Low-probability condition: The median price paid to avoid a 1% chance of a shock was $7, substantially greater than the median price paid to avoid a 1% chance of a $20 penalty.
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.
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 ...
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 difference is how much the representation of the facts has been compressed by assuming that H is true. This is the evidence that the hypothesis H is true. If () is estimated from encoding length then the probability obtained will not be between 0 and 1. The value obtained is proportional to the probability, without being a good probability ...
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.
The distinction between ambiguity aversion and risk aversion is important but subtle. Risk aversion comes from a situation where a probability can be assigned to each possible outcome of a situation and it is defined by the preference between a risky alternative and its expected value. Ambiguity aversion applies to a situation when the ...