The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so that the posterior distributions converge at the optimal rate without prior knowledge of the degree of smoothness of the density function or the regression function to be estimated.
"Convergence rates for posterior distributions and adaptive estimation." Ann. Statist. 32 (4) 1556 - 1593, August 2004. https://doi.org/10.1214/009053604000000490