Paulo, Rui Default priors for Gaussioan processes. (English) Zbl 1069.62030 Ann. Stat. 33, No. 2, 556-582 (2005). Summary: Motivated by the statistical evaluation of complex computer models, we deal with the issue of objective prior specification for the parameters of Gaussian processes. In particular, we derive the Jeffreys-rule, independence Jeffreys and reference priors for this situation, and prove that the resulting posterior distributions are proper under a quite general set of conditions. A proper flat prior strategy, based on maximum likelihood estimates, is also considered, and all priors are then compared on the grounds of the frequentist properties of the ensuing Bayesian procedures. Computational issues are also addressed in the paper, and we illustrate the proposed solutions by means of an example taken from the field of complex computer model validation. Cited in 1 ReviewCited in 35 Documents MSC: 62F15 Bayesian inference 62M30 Inference from spatial processes 62F10 Point estimation 60G15 Gaussian processes 68U20 Simulation (MSC2010) 62H12 Estimation in multivariate analysis Keywords:Jeffreys prior; reference prior; integrated likelihood; frequentist coverage; posterior propriety Software:BayesDA × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Bayarri, M. J., Berger, J. O., Higdon, D., Kennedy, M. C., Kottas, A., Paulo, R., Sacks, J., Cafeo, J. A., Cavendish, J., Lin, C. H. and Tu, J. (2002). A framework for validation of computer models. Technical Report 128, National Institute of Statistical Sciences. [2] Berger, J. O. and Bernardo, J. M. (1992). On the development of reference priors (with discussion). In Bayesian Statistics 4 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 35–60. Oxford Univ. Press. [3] Berger, J. O., De Oliveira, V. and Sansó, B. (2001). Objective Bayesian analysis of spatially correlated data. J. Amer. Statist. Assoc. 96 1361–1374. · Zbl 1051.62095 · doi:10.1198/016214501753382282 [4] Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion). J. Roy. Statist. Soc. Ser. B 41 113–147. · Zbl 0428.62004 [5] Cressie, N. A. C. (1993). Statistics for Spatial Data , revised ed. Wiley, New York. · Zbl 0825.62477 [6] Fuentes, M. (2003). Testing for separability of spatio-temporal covariance functions. Technical Report 2545, Dept. Statistics, North Carolina State Univ. [7] Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (1995). Bayesian Data Analysis . Chapman and Hall, London. · Zbl 1279.62004 [8] Harville, D. A. (1974). Bayesian inference for variance components using only error contrasts. Biometrika 61 383–385. · Zbl 0281.62072 · doi:10.1093/biomet/61.2.383 [9] Harville, D. A. (1997). Matrix Algebra from a Statistician ’ s Perspective . Springer, Berlin. · Zbl 0881.15001 [10] Kass, R. and Wasserman, L. (1996). The selection of prior distributions by formal rules. J. Amer. Statist. Assoc. 91 1343–1370. · Zbl 0884.62007 · doi:10.2307/2291752 [11] Kennedy, M. C. and O’Hagan, A. (2000). Predicting the output from a complex computer code when fast approximations are available. Biometrika 87 1–13. · Zbl 0974.62024 · doi:10.1093/biomet/87.1.1 [12] Kennedy, M. C. and O’Hagan, A. (2001). Bayesian calibration of computer models. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 425–464. · Zbl 1007.62021 · doi:10.1111/1467-9868.00294 [13] 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. · Zbl 0955.62619 [14] Short, M. and Carlin, B. (2003). Multivariate spatiotemporal CDFs with measurement error. Technical Report 2003-015, Division of Biostatistics, Univ. Minnesota. · Zbl 1331.62447 [15] Tong, Y. L. (1990). The Multivariate Normal Distribution . Springer, Berlin. · Zbl 0689.62036 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.