On frequentist coverage of Bayesian credible sets for estimation of the mean under constraints

Frequentist coverage of $(1-\alpha )$-highest posterior density (HPD) credible sets is studied in a signal plus noise model under a large class of noise distributions. We consider a specific class of spike-and-slab prior distributions. Different regimes are identified and we derive closed form expressions for the $(1-\alpha )$-HPD on each of these regimes. Similar to the earlier work by Marchand and Strawderman, it is shown that under suitable conditions, the frequentist coverage can drop to $1-3\alpha \mathrm{/}2.$