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where <math> m</math> is the mean function and <math> C </math> is the covariance function. Popular mean functions are low order polynomials and a popular [[covariance function]] is [[Matern covariance]], which includes both the exponential (<math> \nu = 1/2 </math>) and Gaussian covariances (as <math> \nu \rightarrow \infty </math>).
==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 [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ss/1177012413] and distance based criteria[http://www.sciencedirect.com/science/article/pii/037837589090122B].
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