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Computer experiments. (English) Zbl 0919.62089
Ghosh, S. (ed.) et al., Design and analysis of experiments. Amsterdam: North-Holland. Handb. Stat. 13, 261-308 (1996).
The authors present a discussion of the two main statistical approaches to computer experiments: Gaussian processes and random input. The basic goals of computer experiments are optimization, visualization, approximation, and integration of a function which is itself the output of a computer program, which depends on a large number of input variables and which is costly to evaluate. The first approach uses Bayesian prediction and inference like kriging when the function is assumed to be the realization of a Gaussian random field. Various Bayesian designs are discussed including entropy and mean squared error based designs, maximin and minimax designs, and hyperbolic cross points.
The second approach arises from frequentist prediction and inference when errors or randomness are assumed in the input variables. In this framework more regular designs like grids, good lattice points, Latin hypercubes, randomized orthogonal arrays and scrambled nets turn out to be efficient. Both concepts are illustrated by selected applications.
For the entire collection see [Zbl 0897.00015].
Reviewer: R.Schwabe (Berlin)

62K99 Design of statistical experiments
62K05 Optimal statistical designs
65C99 Probabilistic methods, stochastic differential equations
62F15 Bayesian inference
65D15 Algorithms for approximation of functions
65D30 Numerical integration