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Default priors for Gaussioan processes. (English) Zbl 1069.62030

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.

MSC:

62F15 Bayesian inference
62M30 Inference from spatial processes
62F10 Point estimation
60G15 Gaussian processes
68U20 Simulation (MSC2010)
62H12 Estimation in multivariate analysis

Software:

BayesDA
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References:

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