DEFAULT PRIORS FOR GAUSSIAN PROCESSES By Rui Paulo
نویسنده
چکیده
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. Another prior specification 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. ∗Research was supported by the U.S. National Science Foundation, Grants DMS-0073952 at the National Institute of Statistical Sciences, DMS-0103265, and the Statistical and Applied Mathematical Sciences Institute. This research formed part of the author’s Ph.D. thesis at Duke University, where he was partly supported by a Ph.D. Fellowship awarded by Fundação para a Ciência e a Tecnologia, Portugal, with reference PRAXIS XXI/BD/15703/98.
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Default Priors for Gaussian Processes
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...
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