Predicting the output from a complex computer code when fast approximations are available

Biometrika

Volumn 87, Issue 1, 2000, Pages 1-13

  Kennedy, M C ^a   O'Hagan, A ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Bayesian uncertainty analysis; Computer experiment; Gaussian process; Multi level code

Indexed keywords

EID: 0007312235     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/87.1.1     Document Type: Article

References (19)

1. ASLETT, R., BUCK, R. J., DUVALL, S. G., SACKS, J. & WELCH, W. J. (1998). Circuit optimization via sequential computer experiments. Design of an output buffer. Appl. Statist. 47, 31-48.
2. BLIGHT, B. J. N. & OTT, L. (1975). A Bayesian approach to model inadequacy for polynomial regression. Biometrika 62, 79-88.
3. CRAIG, P. S., GOLDSTEIN, M., SEHEULT, A. H. & SMITH, J. A. (1996). Bayes linear strategies for matching hydrocarbon reservoir history. In Bayesian Statistics 5, Ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, pp. 69-95. Oxford University Press.
4. CRESSIE, N. & HAWKINS, D. M. (1980). Robust estimation of the variogram, I. J. Int. Assoc. Math. Geol. 12, 115-25.
5. CURRIN, C., MITCHELL, T., MORRIS, M. & YLVISAKER, D. (1991). Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. J. Am. Statist. Assoc. 86, 953-63.
6. DIACONIS, P. (1988). Bayesian numerical analysis. In Statistical Decision Theory and Related Topics IV, Ed. S. S. Gupta and J. Berger, pp. 163-75. New York: Springer.
7. HAYLOCK, R. & O'HAGAN, A. (1996). On inference for outputs of computationally expensive algorithms with uncertainty on the inputs. In Bayesian Statistics 5, Ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, pp. 629-37. Oxford University Press.
8. KIMELDORF, G. S. & WAHBA, G. (1970). A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. Ann. Math. Statist. 41, 495-502.
9. MATÉRN, B. (1986). Spatial Variation, 2nd ed., Lecture Notes in Statistics Vol. 36. New York: Springer-Verlag.
10. MORRIS, M. D., MITCHELL, T. J. & YLVISAKER, D. (1993). Bayesian design and analysis of computer experiments: use of derivatives in surface prediction. Technometrics 35, 243-55.
11. NEAL, R. M. (1999). Regression and classification using Gaussian process priors (with Discussion). In Bayesian Statistics 6, Ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, pp. 475-501. Oxford University Press.
12. O'HAGAN, A. (1978). Curve fitting and optimal design for prediction (with Discussion). J. R. Statist. Soc. B 40, 1-42.
13. O'HAGAN, A. (1991). Bayes-Hermite quadrature. J. Statist. Plan. Infer. 29, 245-60.
14. O'HAGAN, A. (1992). Some Bayesian numerical analysis (with Discussion). In Bayesian Statistics 4, Ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, pp. 345-63. Oxford University Press.
15. O'HAGAN, A., KENNEDY, M. C. & OAKLEY, J. E. (1999). Uncertainty analysis and other inference tools for complex computer codes (with Discussion). In Bayesian Statistics 6, Ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, pp. 503-24. Oxford University Press.
16. SACKS, J., WELCH, W. J., MITCHELL, T. J. & WYNN, H. P. (1989). Design and analysis of computer experiments (with Discussion). Statist. Sci. 4, 409-35.
17. SCHOENBERG, I. J. (1938). Metric spaces and completely monotone functions. Ann. Math. 39, 811-41.
18. WELCH, W. J., BUCK, R. J., SACKS, J., WYNN, H. P., MITCHELL, T. J. & MORRIS, M. D. (1992). Screening, predicting, and computer experiments. Technometrics 34, 15-25.
19. YOUNG, P., PARKINSON, S. & LEES, M. (1996). Simplicity out of complexity in environmental modelling: Occam's razor revisited. J. Appl. Statist. 23, 165-210.