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2008 Lower bounds for posterior rates with Gaussian process priors
Ismaël Castillo
Electron. J. Statist. 2: 1281-1299 (2008). DOI: 10.1214/08-EJS273

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.

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Ismaël Castillo. "Lower bounds for posterior rates with Gaussian process priors." Electron. J. Statist. 2 1281 - 1299, 2008. https://doi.org/10.1214/08-EJS273

Information

Published: 2008
First available in Project Euclid: 22 December 2008

zbMATH: 1320.62067
MathSciNet: MR2471287
Digital Object Identifier: 10.1214/08-EJS273

Subjects:
Primary: 62G05 , 62G20

Keywords: Bayesian nonparametrics , Gaussian process priors , lower bounds

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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