Default Priors for Gaussian Processes
05/01/2004 Monday 5th January 2004, 14:30 (Room P4.35, Mathematics Building)
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Rui Paulo, National Institute of Statistical Sciences and Statistical and Applied Mathematical Sciences Institute, North Carolina, USA
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 Jeffreysrule, 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.
