Lower bounds for posterior rates with Gaussian process priors

Abstract

Upper bounds for rates of convergence of posterior distributions associated to Gaussian process priors are obtained by van der Vaart and van Zanten in [14] and expressed in terms of a concentration function involving the Reproducing Kernel Hilbert Space of the Gaussian prior. Here lower-bound counterparts are obtained. As a corollary, we obtain the precise rate of convergence of posteriors for Gaussian priors in various settings. Additionally, we extend the upper-bound results of [14] about Riemann-Liouville priors to a continuous family of parameters.

Published in at http://dx.doi.org/10.1214/08-EJS273 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Rates of contraction of posterior distributions based on Gaussian process priors
• Convergence rates of posterior distributions for noniid observations
• Reproducing kernel Hilbert spaces of Gaussian priors

Cited by in corpus (11)

• Needles and Straw in a Haystack: Posterior concentration for possibly sparse sequences
• On Bayesian supremum norm contraction rates
• A Bernstein-von Mises theorem for smooth functionals in semiparametric models
• Adaptive Bernstein-von Mises theorems in Gaussian white noise
• Anisotropic function estimation using multi-bandwidth Gaussian processes
• Gaussian process methods for one-dimensional diffusions: optimal rates and adaptation
• Bayesian Nonparametric Causal Inference: Information Rates and Learning Algorithms
• Semiparametric Bayesian causal inference
• Rate-optimal posterior contraction for sparse PCA
• Bayesian test of normality versus a Dirichlet process mixture alternative
• Designing truncated priors for direct and inverse Bayesian problems