The Annals of Statistics

Default priors for Gaussian processes

Rui Paulo

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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.

Article information

Ann. Statist., Volume 33, Number 2 (2005), 556-582.

First available in Project Euclid: 26 May 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference
Secondary: 62M30: Spatial processes 60G15: Gaussian processes

Gaussian process Jeffreys prior reference prior integrated likelihood frequentist coverage posterior propriety computer model


Paulo, Rui. Default priors for Gaussian processes. Ann. Statist. 33 (2005), no. 2, 556--582. doi:10.1214/009053604000001264.

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