## Bernoulli

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

### Spike and slab empirical Bayes sparse credible sets

#### 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.

#### Article information

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

Dates
Revised: January 2019
First available in Project Euclid: 26 November 2019

https://projecteuclid.org/euclid.bj/1574758824

Digital Object Identifier
doi:10.3150/19-BEJ1119

Mathematical Reviews number (MathSciNet)
MR4036030

Zentralblatt MATH identifier
07140495

#### Citation

Castillo, Ismaël; Szabó, Botond. Spike and slab empirical Bayes sparse credible sets. Bernoulli 26 (2020), no. 1, 127--158. doi:10.3150/19-BEJ1119. https://projecteuclid.org/euclid.bj/1574758824

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#### Supplemental materials

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