In real life applications, both kinds of uncertainties are present. Uncertainty quantification intends to explicitly express both types of uncertainty separately. The quantification for the aleatoric uncertainties can be relatively straightforward, where traditional (frequentist) probability is the most basic form. 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, 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 understand the (lack of) knowledge of the system, process or mechanism. Representation of epistemic uncertainty can be based on methods such as probability bounds analysis, fuzzy logic or evidence/belief theories such as subjective logic or Dempster–Shafer theory (where epistemic uncertainty is represented as vacuity of belief).