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A novel block prior is proposed for adaptive Bayesian estimation. The priordoes not depend on the smoothness of the function or the sample size. It putssufficient prior mass near the true signal and automatically concentrates onits effective dimension. A rate-optimal posterior contraction is obtained in ageneral framework, which includes density estimation, white noise model,Gaussian sequence model, Gaussian regression and spectral density estimation.

Rate exact Bayesian adaptation with modified block priors