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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.
where is the value function (typical form shown in Figure 1), is the weighting function (as sketched in Figure 2) and ():=, i.e. the integral of the probability measure over all values up to , is the cumulative probability. This generalizes the original formulation by Tversky and Kahneman from finitely many distinct outcomes to infinite (i.e ...
The uncertainty effect, also known as direct risk aversion, is a phenomenon from economics and psychology which suggests that individuals may be prone to expressing such an extreme distaste for risk that they ascribe a lower value to a risky prospect (e.g., a lottery for which outcomes and their corresponding probabilities are known) than its worst possible realization.
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.
Uncertainty is an unavoidable aspect of everyday life. The degree to which it is felt in a given situation varies among individuals. Because uncertainty is dependent upon perspective, "a person who believes himself or herself to be uncertain is uncertain." [2] However, people have different appetites and tolerances for uncertainty. For some ...
For example, the 68% confidence limits for a one-dimensional variable belonging to a normal distribution are approximately ± one standard deviation σ from the central value x, which means that the region x ± σ will cover the true value in roughly 68% of cases. If the uncertainties are correlated then covariance must be taken into account ...
Regret is a negative emotion with a powerful social and reputational component, and is central to how humans learn from experience and to the human psychology of risk aversion. Conscious anticipation of regret creates a feedback loop that transcends regret from the emotional realm—often modeled as mere human behavior —into the realm of the ...
Uncertainty is traditionally modelled by a probability distribution, as developed by Kolmogorov, [1] Laplace, de Finetti, [2] Ramsey, Cox, Lindley, and many others.However, this has not been unanimously accepted by scientists, statisticians, and probabilists: it has been argued that some modification or broadening of probability theory is required, because one may not always be able to provide ...