Bayesian inference with rescaled Gaussian process priors
Statistics Theory
2009-09-29 v1 Statistics Theory
Abstract
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit rescaled Gaussian process priors yielding posteriors that contract around the true parameter at optimal convergence rates. To derive our results we establish bounds on small deviation probabilities for smooth stationary Gaussian processes.
Cite
@article{arxiv.0710.3679,
title = {Bayesian inference with rescaled Gaussian process priors},
author = {Aad van der Vaart and Harry van Zanten},
journal= {arXiv preprint arXiv:0710.3679},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/07-EJS098 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)