Adaptive posterior contraction rates for the horseshoe
By Stéphanie van der Pas, Botond Szab'o, A. van der Vaart. 2017
87 citations recorded by the source corpus.
We investigate the frequentist properties of Bayesian procedures for estimation based on the horseshoe prior in the sparse multivariate normal means model. Previous theoretical results assumed that the sparsity level, that is, the number of signals, was known. We drop this assumption and characterize the behavior of the maximum marginal likelihood estimator (MMLE) of a key parameter of the horseshoe prior. We prove that the MMLE is an effective estimator of the sparsity level, in the sense that it leads to (near) minimax optimal estimation of the underlying mean vector generating the data. Besides this empirical Bayes procedure, we consider the hierarchical Bayes method of putting a prior on the unknown sparsity level as well. We show that both Bayesian techniques lead to rate-adaptive optimal posterior contraction, which implies that the horseshoe posterior is a good candidate for generating rate-adaptive credible sets.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/911edbab575f58f9dbe4812aaafe9757e7077a7f
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In Statistics and Probability
- Botond Szab'o
- Stéphanie van der Pas
- A. van der Vaart
- Judith Rousseau
- Kolyan Ray
- Richard Nickl
- Shahar Mendelson
- Vladimir Koltchinskii
Citations in the corpus
- Uncertainty Quantification for the Horseshoe (with Discussion) (2016, methodology): “The upper bounds on the contraction rates of the horseshoe posterior distributions given in van der Pas et al. (2017a) imply that the horseshoe credible sets are narrow enough to be informative.”