Before revision:  The general theorem is applied to standard Gaussian priors , which are shown to converge to the truth at the minimax optimal rate over Sobolev smoothness classes in any dimension . We further establish contraction rates for p-exponential priors over spatially inhomogeneous Besov function classes for which Gaussian priors are unsuitable, again in any dimension.
After revision:  The general theorem is applied to standard Gaussian priors , which are shown to converge to the truth at the minimax optimal rate over Sobolev smoothness classes in any dimension