Abstract
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 $q\le2$. 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.
Citation
Ismaël Castillo. Botond Szabó. "Spike and slab empirical Bayes sparse credible sets." Bernoulli 26 (1) 127 - 158, February 2020. https://doi.org/10.3150/19-BEJ1119
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