Uncertainty quantification

Uncertainty quantification (UQ) is the science of quantitative characterization and reduction 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 example would be to predict the acceleration of a human body in a head-on crash with another car: even if we exactly knew the speed, small differences in the manufacturing of individual cars, how tightly every bolt has been tightened, etc., will lead to different results that can only be predicted in a statistical sense.

Many problems in the natural sciences and engineering are also rife with sources of uncertainty. Computer experiments on computer simulations are the most common approach to study problems in uncertainty quantification.

Uncertainty can enter mathematical models and experimental measurements in various contexts. One way to categorize the sources of uncertainty is to consider:

It is sometimes assumed that uncertainty can be classified into two categories, although the validity of this categorization is open to debate. These categories are prominently seen in medical applications.

In real life applications, both kinds of uncertainties are present. Uncertainty quantification intends to work toward reducing epistemic uncertainties to aleatoric uncertainties. The quantification for the aleatoric uncertainties can be relatively straightforward to perform, depending on the application. Techniques such as the Monte Carlo method are frequently used. A probability distribution can be represented by its moments (in the Gaussian case, the mean and covariance suffice, although it should be noted that, in general, even knowledge of all moments to arbitrarily high order still does not specify the distribution function uniquely), or more recently, by techniques such as Karhunen–Loève and polynomial chaos expansions. To evaluate epistemic uncertainties, the efforts are made to gain better knowledge of the system, process or mechanism. Methods such as fuzzy logic or evidence theory (Dempster–Shafer theory – a generalization of the Bayesian theory of subjective probability) are used.

...
Wikipedia