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2015 Adaptive Bayesian credible sets in regression with a Gaussian process prior
Suzanne Sniekers, Aad van der Vaart
Electron. J. Statist. 9(2): 2475-2527 (2015). DOI: 10.1214/15-EJS1078


We investigate two empirical Bayes methods and a hierarchical Bayes method for adapting the scale of a Gaussian process prior in a nonparametric regression model. We show that all methods lead to a posterior contraction rate that adapts to the smoothness of the true regression function. Furthermore, we show that the corresponding credible sets cover the true regression function whenever this function satisfies a certain extrapolation condition. This condition depends on the specific method, but is implied by a condition of self-similarity. The latter condition is shown to be satisfied with probability one under the prior distribution.


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Suzanne Sniekers. Aad van der Vaart. "Adaptive Bayesian credible sets in regression with a Gaussian process prior." Electron. J. Statist. 9 (2) 2475 - 2527, 2015.


Received: 1 April 2015; Published: 2015
First available in Project Euclid: 19 November 2015

zbMATH: 1327.62300
MathSciNet: MR3425364
Digital Object Identifier: 10.1214/15-EJS1078

Primary: 62G05, 62G15
Secondary: 62G20

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 2 • 2015
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