Open Access
VOL. 3 | 2008 Reproducing kernel Hilbert spaces of Gaussian priors
J. H. van Zanten, A. W. van der Vaart

Editor(s) Bertrand Clarke, Subhashis Ghosal

Inst. Math. Stat. (IMS) Collect., 2008: 200-222 (2008) DOI: 10.1214/074921708000000156


We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described through a concentration function that is expressed in the reproducing Hilbert space. Absolute continuity of Gaussian measures and concentration inequalities play an important role in understanding and deriving this result. Series expansions of Gaussian variables and transformations of their reproducing kernel Hilbert spaces under linear maps are useful tools to compute the concentration function.


Published: 1 January 2008
First available in Project Euclid: 28 April 2008

MathSciNet: MR2459226

Digital Object Identifier: 10.1214/074921708000000156

Primary: 60G15 , 62G05

Keywords: Bayesian inference , rate of convergence

Rights: Copyright © 2008, Institute of Mathematical Statistics

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