the expected value of system responses) also requires numerical integration. Markov chain Monte Carlo (MCMC) is often used for integration; however it is computationally expensive. The fully Bayesian approach requires a huge amount of calculations and may not yet be practical for dealing with the most complicated modelling situations. Known issues The theories and methodologies for uncertainty propagation are much better established, compared with inverse uncertainty quantification. For the latter, several difficulties remain unsolved: Dimensionality issue: The computational cost increases dramatically with the dimensionality of the problem, i.e. the number of input variables and/or the number of unknown parameters. Identifiability issue: Multiple combinations of unknown parameters and discrepancy function can yield the same experimental prediction. Hence different values of parameters cannot be distinguished/identified. This issue is circumvented in a Bayesian approach, where such combinations are averaged over. Incomplete model response: Refers to a model not having a solution for some combinations of the input variables. See also Computer experiment Further research is needed Quantification of margins and uncertainties Probabilistic numerics Bayesian regression Bayesian probability References Applied mathematics Mathematical modeling Operations research Statistical theory