Lower bounds for posterior rates with Gaussian process priors

Details Lower bounds for posterior rates with Gaussian process priors Lower bounds for posterior rates with Gaussian process priors

2008-07-17

arxiv.org/abs/0807.2734v2

Electronic Journal of Statistics 2008, Vol. 2, 1281-1299

Mathematics

Statistics Theory

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

Scientific paper

10.1214/08-EJS273

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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