In statistics, Gaussian process emulator is one name for a general type of

statistical model A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, ...

that has been used in contexts where the problem is to make maximum use of the outputs of a complicated (often non-random) computer-based simulation model. Each run of the simulation model is computationally expensive and each run is based on many different controlling inputs. The variation of the outputs of the simulation model is expected to vary reasonably smoothly with the inputs, but in an unknown way. The overall analysis involves two models: the simulation model, or "simulator", and the statistical model, or "emulator", which notionally emulates the unknown outputs from the simulator. The Gaussian process emulator model treats the problem from the viewpoint of

Bayesian statistics Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, ...

. In this approach, even though the output of the simulation model is fixed for any given set of inputs, the actual outputs are unknown unless the computer model is run and hence can be made the subject of a

Bayesian analysis Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and ...

. The main element of the Gaussian process emulator model is that it models the outputs as a

Gaussian process In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. ...

on a space that is defined by the model inputs. The model includes a description of the correlation or covariance of the outputs, which enables the model to encompass the idea that differences in the output will be small if there are only small differences in the inputs.

References

*Currin, C., Mitchell, T., Morris, M., and Ylvisaker, D. (1991) "Bayesian Prediction of Deterministic Functions, with Applications to the Design and Analysis of Computer Experiments,"

Journal of the American Statistical Association The ''Journal of the American Statistical Association (JASA)'' is the primary journal published by the American Statistical Association, the main professional body for statisticians in the United States. It is published four times a year in Ma ...

, 86, 953–963. *Kimeldorf, G. S. and Wahba, G. (1970) "A correspondence between Bayesian estimation on stochastic processes and smoothing by splines," The Annals of Mathematical Statistics, 41, 495–502. *O'Hagan, A. (1978) "Curve fitting and optimal design for predictions,"

Journal of the Royal Statistical Society The ''Journal of the Royal Statistical Society'' is a peer-reviewed scientific journal of statistics. It comprises three series and is published by Wiley for the Royal Statistical Society. History The Statistical Society of London was founde ...

B, 40, 1–42. *O'Hagan, A. (2006) "Bayesian analysis of computer code outputs: A tutorial," Reliability Engineering & System Safety, 91, 1290–1300. *Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989) "Design and Analysis of Computer Experiments,"

Statistical Science ''Statistical Science'' is a review journal published by the Institute of Mathematical Statistics. The founding editor was Morris H. DeGroot, who explained the mission of the journal in his 1986 editorial: "A central purpose of ''Statistical S ...

, 4, 409–423. {{Statistics Ensemble learning Statistical randomness Statistics articles needing expert attention Bayesian statistics

See also

References