uncertainty can also occur simultaneously in a single term E.g., when experimental parameters show aleatoric uncertainty, and those experimental parameters are input to a computer simulation. If then for the uncertainty quantification a surrogate model, e.g. a Gaussian process or a Polynomial Chaos Expansion, is learnt from computer experiments, this surrogate exhibits epistemic uncertainty that depends on or interacts with the aleatoric uncertainty of the experimental parameters. Such an uncertainty cannot solely be classified as aleatoric or epistemic any more, but is a more general inferential uncertainty. 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. Epistemic uncertainty is generally understood through the lens of Bayesian probability, where probabilities are interpreted as indicating how certain a rational person could be regarding a specific claim. Mathematical perspective In mathematics, uncertainty is often characterized in terms of a probability distribution. From that perspective, epistemic uncertainty means not being certain what the relevant probability distribution is, and aleatoric uncertainty means not being certain what a random sample drawn from a probability distribution will be. Types of problems 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 model parameters are calibrated simultaneously using test data). There has been a proliferation of research on the former problem and a majority of uncertainty analysis techniques were developed for it. On the other hand, the latter problem is drawing increasing attention in the engineering design community, since uncertainty quantification of a model and the subsequent predictions of the true system response(s) are of