Open Access
June 2008 Rates of contraction of posterior distributions based on Gaussian process priors
A. W. van der Vaart, J. H. van Zanten
Ann. Statist. 36(3): 1435-1463 (June 2008). DOI: 10.1214/009053607000000613


We derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on Gaussian processes. The rate of contraction is shown to depend on the position of the true parameter relative to the reproducing kernel Hilbert space of the Gaussian process and the small ball probabilities of the Gaussian process. We determine these quantities for a range of examples of Gaussian priors and in several statistical settings. For instance, we consider the rate of contraction of the posterior distribution based on sampling from a smooth density model when the prior models the log density as a (fractionally integrated) Brownian motion. We also consider regression with Gaussian errors and smooth classification under a logistic or probit link function combined with various priors.


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A. W. van der Vaart. J. H. van Zanten. "Rates of contraction of posterior distributions based on Gaussian process priors." Ann. Statist. 36 (3) 1435 - 1463, June 2008.


Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1141.60018
MathSciNet: MR2418663
Digital Object Identifier: 10.1214/009053607000000613

Primary: 60G15 , 62G05

Keywords: Bayesian inference , ‎classification‎ , Nonparametric density estimation , Nonparametric regression , rate of convergence

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 3 • June 2008
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