  In the general signal+noise model we construct an empirical Bayes posterior
which we then use for uncertainty quantification for the unknown, possibly
sparse, signal. We introduce a novel excessive bias restriction (EBR)
condition, which gives rise to a new slicing of the entire space that is
suitable for uncertainty quantification. Under EBR and some mild conditions on
the noise, we establish the local (oracle) optimality of the proposed
confidence ball. In passing, we also get the local optimal (oracle) results for
estimation and posterior contraction problems. Adaptive minimax results (also
for the estimation and posterior contraction problems) over various sparsity
classes follow from our local results.
