itself as , and the resulting output as . Both and are vector quantities, and they can be very large collections of values, often indexed by space, or by time, or by both space and time. Although is known in principle, in practice this is not the case. Many simulators comprise tens of thousands of lines of high-level computer code, which is not accessible to intuition. For some simulations, such as climate models, evaluation of the output for a single set of inputs can require millions of computer hours . Gaussian process prior The typical model for a computer code output is a Gaussian process. For notational simplicity, assume is a scalar. Owing to the Bayesian framework, we fix our belief that the function follows a Gaussian process, where is the mean function and is the covariance function. Popular mean functions are low order polynomials and a popular covariance function is Matern covariance, which includes both the exponential () and Gaussian covariances (as ). Design of computer experiments The design of computer experiments has considerable differences from design of experiments for parametric models. Since a Gaussian process prior has an infinite dimensional representation, the concepts of A and D criteria (see Optimal design), which focus on reducing the error in the parameters, cannot be used. Replications would also be wasteful in cases when the computer simulation has no error. Criteria that are used to determine a good experimental design include integrated mean squared prediction error and distance based criteria . Popular strategies for design include latin hypercube sampling and low discrepancy sequences. Problems with massive sample sizes Unlike physical experiments, it is common for computer experiments to have thousands of different input combinations. Because the standard inference requires matrix inversion of a square matrix of the size of the number of samples (), the cost grows on the . Matrix inversion of large, dense matrices can also cause numerical inaccuracies. Currently, this problem is solved by greedy decision tree techniques, allowing effective computations for unlimited dimensionality and sample size patent WO2013055257A1, or avoided by using approximation methods, e.g. . See also Simulation Uncertainty quantification Bayesian statistics Gaussian process emulator Design of experiments Molecular dynamics Monte Carlo method Surrogate model Grey box completion and validation Further reading Computational science Design of experiments Simulation