Lower bounds for posterior rates with Gaussian process priors

Upper bounds for rates of convergence of posterior distributions associated to Gaussian process priors are obtained in [9] 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 [9] about Riemann-Liouville priors to a continuous family of parameters.