Upper bounds for rates of convergence of posterior distributions associated to Gaussian process priors are obtained by van der Vaart and van Zanten in  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  about Riemann-Liouville priors to a continuous family of parameters.
"Lower bounds for posterior rates with Gaussian process priors." Electron. J. Statist. 2 1281 - 1299, 2008. https://doi.org/10.1214/08-EJS273