Electronic Journal of Statistics

Lower bounds for posterior rates with Gaussian process priors

Ismaël Castillo

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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.

Article information

Source
Electron. J. Statist., Volume 2 (2008), 1281-1299.

Dates
First available in Project Euclid: 22 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1229975383

Digital Object Identifier
doi:10.1214/08-EJS273

Mathematical Reviews number (MathSciNet)
MR2471287

Zentralblatt MATH identifier
1320.62067

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties

Keywords
Bayesian nonparametrics Gaussian process priors Lower bounds

Citation

Castillo, Ismaël. Lower bounds for posterior rates with Gaussian process priors. Electron. J. Statist. 2 (2008), 1281--1299. doi:10.1214/08-EJS273. https://projecteuclid.org/euclid.ejs/1229975383


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