Reproducing kernel Hilbert spaces of Gaussian priors
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.
 Publication:

arXiv eprints
 Pub Date:
 May 2008
 arXiv:
 arXiv:0805.3252
 Bibcode:
 2008arXiv0805.3252V
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Operator Algebras;
 Mathematics  Statistics;
 60G15;
 62G05 (Primary)
 EPrint:
 Published in at http://dx.doi.org/10.1214/074921708000000156 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)