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arXiv · 2003.04406

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

Kevin Duisters·Johannes Schmidt-Hieber
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Abstract

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 $1-3\alpha/2.$

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Kevin Duisters, Johannes Schmidt-Hieber. 2020-03-09. On frequentist coverage of Bayesian credible sets for estimation of the mean under constraints. https://arxiv.org/abs/2003.04406

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