Computer model validation with functional output

Annals of Statistics

Volumn 35, Issue 5, 2007, Pages 1874-1906

  Bayarri, M J ^a   Berger, J O ^b   Cafeo, J ^c   Garcia Donato, G ^d   Liu, F ^b   Palomo, J ^e   Parthasarathy, R J ^c   Paulo, R ^f   Sacks, J ^g   Walsh, D ^h  

^a UNIVERSITY OF VALENCIA   (Spain)

^b Duke University   (United States)

^c GENERAL MOTORS CORPORATION   (United States)

^d UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

^e UNIVERSIDAD REY JUAN CARLOS   (Spain)

^f UNIVERSITY OF LISBON   (Portugal)

^g NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES   (United States)

^h MASSEY UNIVERSITY   (New Zealand)

Author keywords

Bayesian analysis; Bias; Computer models; Functional data; Uncertain inputs; Validation

Indexed keywords

EID: 46749084551     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000163     Document Type: Article

References (28)

1. ASLETT, R., BUCK, R. J., DUVALL, S. G., SACKS, J. and WELCH, W. J. (1998). Circuit optimization via sequential computer experiments: Design of an output buffer. Appl. Statist. 47 31-48.
2. BAYARRI, M., BERGER, J., CAFEO, J., GARCIA-DONATO, G., LIU, F., PALOMO, J., PARTHASARATHY, R., PAULO, R., SACKS, J. and WALSH, D. (2006). Computer model validation with functional outputs. Technical Report 165, National Institute of Statistical Sciences.
3. BAYARRI, M. J., BERGER, J. O., KENNEDY, M., KOTTAS, A., PAULO, R., SACKS, J., CAFEO, J. A., LIN, C. H. and TU, J. (2005). Bayesian validation of a computer model for vehicle crashworthiness. Technical Report 163, National Institute of Statistical Sciences.
4. BAYARRI, M. J., BERGER, J. O., PAULO, R., SACKS, J., CAFEO, J. A., CAVENDISH, J., LIN, C.-H. and TU, J. (2007). A framework for validation of computer models. Technometrics 49 138-154.
5. CAFEO, J. and CAVENDISH, J. (2001). A framework for verification and validation of computer models and simulations. Internal General Motors document, GM Research and Development Center.
6. CRAIG, P. S., GOLDSTEIN, M., ROUGIER, J. C. and SEHEULT, A. H. (2001). Bayesian forecasting for complex systems using computer simulators. J. Amer. Statist. Assoc. 96 717-729.
7. CRAIG, P. S., GOLDSTEIN, M., SEHEULT, A. H. and SMITH, J. A. (1997). Pressure matching for hydrocarbon reservoirs: A case study in the use of Bayes linear strategies for large computer experiments (with discussion). In Case Studies in Bayesian Statistics III (C. Gatsonis, J. S. Hodges, R. E. Kass, R. McCulloch, P. Rossi and N. D. Singpurwalla, eds.) 36-93. Springer, New York.
8. 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. J. Amer. Statist. Assoc. 86 953-963.
9. EASTERLING, R. G. (2001). Measuring the predictive capability of computational models: Principles and methods, issues and illustrations. Technical Report SAND2001-0243, Sandia National Laboratories.
10. FUENTES, M., GUTTORP, P. and CHALLENOR, P. (2003). Statistical assessment of numerical models. Internat. Statist. Rev. 71 201-221.
11. GOLDSTEIN, M. and ROUGIER, J. C. (2003). Calibrated Bayesian forecasting using large computer simulators. Technical report, Statistics and Probability Group, Univ. Durham. Available at www.maths.dur.ac.uk/stats/physpred/papers/CalibratedBayesian.ps.
12. GOLDSTEIN, M. and ROUGIER, J. C. (2004). Probabilistic formulations for transferring inferences from mathematical models to physical systems. SIAM J. Sci. Comput. 26 467-487.
13. HIGDON, D., GATTIKER, J., WILLIAMS, B. and RIGHTLEY, M. (2007). Computer model validation using high-dimensional outputs. In Bayesian Statistics 8 (J. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West, eds.). Oxford Univ. Press.
14. KENNEDY, M. C. and O'HAGAN, A. (2001). Bayesian calibration of computer models (with discussion) J. R. Stat. Soc. Ser. B Stat. Methodol. 63 425-464.
15. KENNEDY, M. C., O'HAGAN, A. and HIGGINS, N. (2002). Bayesian analysis of computer code outputs. In Quantitative Methods for Current Environmental Issues (C. W. Anderson, V. Barnett, P. C. Chatwin and A. H. El-Shaarawi, eds.) 227-243. Springer, London.
16. MORRIS, M. D., MITCHELL, T. J. and YLVISAKER, D. (1993). Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction. Technometrics 35 243-255.
17. MORRIS, J., VANNUCCI, M., BROWN, P. and CARROLL, R. (2003). Wavelet-based nonparametric modeling of hierarchical functions in colon carcinogenesis (with discussion). J. Amer. Statist. Assoc. 98 573-597.
18. MÜLLER, P. and VIDAKOVIC, B., eds. (1999). Bayesian Inference in Wavelet-Based Models. Lecture Notes in Statist. 141. Springer, New York.
19. NAGY, B., LOEPPKY, J. and WELCH, W. J. (2007). Fast Bayesian inference for Gaussian process models. Technical Report 230, Dept. Statistics, Univ. British Columbia.
20. OBERKAMPF, W. and TRUCANO, T. (2000). Validation methodology in computational fluid dynamics. Technical Report 2000-2549, American Institute of Aeronautics and Astronautics.
21. PILCH, M., TRUCANO, T., MOYA, J. L., FROEHLICH, G., HODGES, A. and PEERCY, D. (2001). Guidelines for Sandia ASCI verification and validation plans-content and format: Version 2.0. Technical Report SAND 2001-3101, Sandia National Laboratories.
22. ROACHE, P. (1998). Verification and Validation in Computational Science and Engineering. Hermosa, Albuquerque, NM.
23. SACKS, J., WELCH, W. J., MITCHELL, T. J. and WYNN, H. P. (1989). Design and analysis of computer experiments (with discussion). Statist. Sci. 4 409-435.
24. SANTNER, T., WILLIAMS, B. and NOTZ, W. (2003). The Design and Analysis of Computer Experiments. Springer, New York.
25. SCHONLAU, M. and WELCH, W. J. (2005). Screening the input variables to a computer model via analysis of variance and visualization. In Screening Methods for Experimentation in Industry, Drug Discovery and Genetics (A. Dean and S. Lewis, eds.) 308-327. Springer, New York.
26. TRUCANO, T., PILCH, M. and OBERKAMPF, W. O. (2002). General concepts for experimental validation of ASCII code applications. Technical Report SAND 2002-0341, Sandia National Laboratories.
27. VIDAKOVIC, B. (1999). Statistical Modeling by Wavelets. Wiley, New York.
28. WELCH, W. J., BUCK, R. J., SACKS, J., WYNN, H. P., MITCHELL, T. J. and MORRIS, M. D. (1992). Screening, predicting and computer experiments. Technometrics 34 15-25.