Editing Computer experiment (section)

==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 [https://web.archive.org/web/20170918022130/https://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ss%2F1177012413] and distance based criteria [http://www.sciencedirect.com/science/article/pii/037837589090122B].

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 [[Invertible matrix|matrix inversion]] of a square matrix of the size of the number of samples (<math>n</math>), the cost grows on the <math> \mathcal{O} (n^3) </math>.  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 [https://patents.google.com/patent/WO2013055257A1/en patent WO2013055257A1], or avoided by using approximation methods, e.g. [https://wayback.archive-it.org/all/20120130182750/http://www.stat.wisc.edu/~zhiguang/Multistep_AOS.pdf].