In this paper we derive adaptive non-parametric rates of concentration of the posterior distributions for the density model on the class of Sobolev and Besov spaces. For this purpose, we build prior models based on wavelet or Fourier expansions of the logarithm of the density. The prior models are not necessarily Gaussian.
"Posterior Concentration Rates for Infinite Dimensional Exponential Families." Bayesian Anal. 7 (2) 311 - 334, June 2012. https://doi.org/10.1214/12-BA710