  In the sparse normal means model, coverage of adaptive Bayesian posterior
credible sets associated to spike and slab prior distributions is considered.
The key sparsity hyperparameter is calibrated via marginal maximum likelihood
empirical Bayes. First, adaptive posterior contraction rates are derived with
respect to $d_q$--type--distances for $q\leq 2$. Next, under a type of
so-called excessive-bias conditions, credible sets are constructed that have
coverage of the true parameter at prescribed $1-\alpha$ confidence level and at
the same time are of optimal diameter. We also prove that the previous
conditions cannot be significantly weakened from the minimax perspective.
