Institute of Mathematical Statistics Collections
- Collections
- Volume 3, 2008, 200-222
Reproducing kernel Hilbert spaces of Gaussian priors
J. H. van Zanten and A. W. van der Vaart
Abstract
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.
Chapter information
Source
Dates
First available in Project Euclid: 28 April 2008
Permanent link to this document
https://projecteuclid.org/euclid.imsc/1209398470
Digital Object Identifier
doi:10.1214/074921708000000156
Mathematical Reviews number (MathSciNet)
MR2459226
Subjects
Primary: 60G15: Gaussian processes 62G05: Estimation
Keywords
Bayesian inference rate of convergence
Rights
Copyright © 2008, Institute of Mathematical Statistics
Citation
van der Vaart, A. W.; van Zanten, J. H. Reproducing kernel Hilbert spaces of Gaussian priors. Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, 200--222, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/074921708000000156. https://projecteuclid.org/euclid.imsc/1209398470
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