• Bernoulli
  • Volume 26, Number 1 (2020), 127-158.

Spike and slab empirical Bayes sparse credible sets

Ismaël Castillo and Botond Szabó

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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.

Article information

Bernoulli, Volume 26, Number 1 (2020), 127-158.

Received: August 2018
Revised: January 2019
First available in Project Euclid: 26 November 2019

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Zentralblatt MATH identifier

convergence rates of posterior distributions credible sets empirical Bayes spike and slab prior distributions


Castillo, Ismaël; Szabó, Botond. Spike and slab empirical Bayes sparse credible sets. Bernoulli 26 (2020), no. 1, 127--158. doi:10.3150/19-BEJ1119.

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Supplemental materials

  • Supplement to “Spike and slab empirical Bayes sparse credible sets”. A separate supplement collects the remaining proofs.