Default priors for Gaussian processes

Details Default priors for Gaussian processes Default priors for Gaussian processes

2005-05-27

arxiv.org/abs/math/0505603v1

Annals of Statistics 2005, Vol. 33, No. 2, 556-582

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000001264 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000001264

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.

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