On frequentist coverage of Bayesian credible sets for estimation of the mean under constraints
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Frequentist coverage of (1-α)-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-α)-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 1-3α/2.
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