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There are two major types of problems in uncertainty quantification: one is the forward propagation of uncertainty (where the various sources of uncertainty are propagated through the model to predict the overall uncertainty in the system response) and the other is the inverse assessment of model uncertainty and parameter uncertainty (where the ...
The symbol ∂z / ∂x 1 represents the "partial derivative" of the function z with respect to one of the several variables x that affect z. For the present purpose, finding this derivative consists of holding constant all variables other than the one with respect to which the partial is being found, and then finding the first derivative in the ...
When the errors on x are uncorrelated, the general expression simplifies to =, where = is the variance of k-th element of the x vector. Note that even though the errors on x may be uncorrelated, the errors on f are in general correlated; in other words, even if Σ x {\displaystyle {\boldsymbol {\Sigma }}^{x}} is a diagonal matrix, Σ f ...
Uncertainty on correlation parameters is another important source of model risk. Cont and Deguest propose a method for computing model risk exposures in multi-asset equity derivatives and show that options which depend on the worst or best performances in a basket (so called rainbow option) are more exposed to model uncertainty than index options.
Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in various fields of science, engineering, and mathematics, such as physics, chemistry, biology, statistics ...
Model uncertainty arises due to the limitations of the forecast model. The process of representing the atmosphere in a computer model involves many simplifications such as the development of parametrisation schemes, which introduce errors into the forecast. Several techniques to represent model uncertainty have been proposed.
Relative uncertainty is the measurement uncertainty relative to the magnitude of a particular single choice for the value for the measured quantity, when this choice is nonzero. This particular single choice is usually called the measured value, which may be optimal in some well-defined sense (e.g., a mean, median, or mode). Thus, the relative ...
For EVIU this other decision is made when the uncertainty is ignored, although it is there, while for EVPI this other decision is made after the uncertainty is removed by obtaining perfect information about x. The EVPI is the expected cost of being uncertain about x, while the EVIU is the additional expected cost of assuming that one is certain.