Uncertainty quantification for the horseshoe

Understand

We investigate the credible sets and marginal credible intervals resulting from the horseshoe prior in the sparse multivariate normal means model.

• We do so in an adaptive setting without assuming knowledge of the sparsity level (number of signals).
• We consider both the hierarchical Bayes method of putting a prior on the unknown sparsity level and the empirical Bayes method with the sparsity level estimated by maximum marginal likelihood.
• We show that credible balls and marginal credible intervals have good frequentist coverage and optimal size if the sparsity level of the prior is set correctly.