Design and analysis of computer experiments. With comments and a rejoinder by the authors. (English) Zbl 0955.62619

Sacks, Jerome; Welch, William J.; Mitchell, Toby J.; Wynn, Henry P.

Stat. Sci. 4, No. 4, 409-435 (1989).

Summary: Many scientific phenomena are now investigated by complex computer models or codes. A computer experiment is a number of runs of the code with various inputs. A feature of many computer experiments is that the output is deterministic—rerunning the code with the same inputs gives identical observations. Often, the codes are computationally expensive to run, and a common objective of an experiment is to fit a cheaper predictor of the output to the data. Our approach is to model the deterministic output as the realization of a stochastic process, thereby providing a statistical basis for designing experiments (choosing the inputs) for efficient prediction. With this model, estimates of uncertainty of predictions are also available. Recent work in this area is reviewed, a number of applications are discussed, and we demonstrate our methodology with an example.

MSC:

62K99	Design of statistical experiments
62J02	General nonlinear regression
62M30	Inference from spatial processes