Bayesian inference with rescaled Gaussian process priors

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.

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)

References in corpus (1)

• Reproducing kernel Hilbert spaces of Gaussian priors

Cited by in corpus (2)

• Adaptive Bayesian estimation using a Gaussian random field with inverse Gamma bandwidth
• Small Deviation Probability via Chaining