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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.
The model used to convert the measurements into the derived quantity is usually based on fundamental principles of a science or engineering discipline. The uncertainty has two components, namely, bias (related to accuracy) and the unavoidable random variation that occurs when making repeated measurements (related to precision).
In physical experiments uncertainty analysis, or experimental uncertainty assessment, deals with assessing the uncertainty in a measurement.An experiment designed to determine an effect, demonstrate a law, or estimate the numerical value of a physical variable will be affected by errors due to instrumentation, methodology, presence of confounding effects and so on.
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 ...
The methodology deals with models whose results are expressed as probability distributions of possible outcomes, often in the form of Monte Carlo simulations, and the problem can be viewed as assessing, and comparing between models, how good these representations of uncertainty are.
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.
Figure 1. Probabilistic parameters of a hidden Markov model (example) X — states y — possible observations a — state transition probabilities b — output probabilities. In its discrete form, a hidden Markov process can be visualized as a generalization of the urn problem with replacement (where each item from the urn is returned to the original urn before the next step). [7]