Open Access
February 2020 Spike and slab empirical Bayes sparse credible sets
Ismaël Castillo, Botond Szabó
Bernoulli 26(1): 127-158 (February 2020). DOI: 10.3150/19-BEJ1119


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.


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Ismaël Castillo. Botond Szabó. "Spike and slab empirical Bayes sparse credible sets." Bernoulli 26 (1) 127 - 158, February 2020.


Received: 1 August 2018; Revised: 1 January 2019; Published: February 2020
First available in Project Euclid: 26 November 2019

zbMATH: 07140495
MathSciNet: MR4036030
Digital Object Identifier: 10.3150/19-BEJ1119

Keywords: Convergence rates of posterior distributions , credible sets , Empirical Bayes , spike and slab prior distributions

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 1 • February 2020
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