Abstract: We apply a Bayesian approach to the problem of estimating a signal observed in the White noise model and we study the rate at which the posterior distribution, the main quantity of interest in Bayesian analysis, concentrates around the true value of the signal. A new benchmark for the posterior concentration rate, the so called posterior oracle rate, is proposed and studied. This is the smallest possible rate over a family of posterior rates corresponding to an appropriately chosen family of priors. To complement the upper bound results on the posterior concentration rate, we establish a lower bound result for the oracle rate. We also study implications for the model selection problem and present some simulations.
