{"paper":{"title":"The Inverse Gamma-Gamma Prior for Optimal Posterior Contraction and Multiple Hypothesis Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Malay Ghosh, Ray Bai","submitted_at":"2017-10-12T05:08:47Z","abstract_excerpt":"We study the well-known problem of estimating a sparse $n$-dimensional unknown mean vector $\\theta = (\\theta_1, ..., \\theta_n)$ with entries corrupted by Gaussian white noise. In the Bayesian framework, continuous shrinkage priors which can be expressed as scale-mixture normal densities are popular for obtaining sparse estimates of $\\theta$. In this article, we introduce a new fully Bayesian scale-mixture prior known as the inverse gamma-gamma (IGG) prior. We prove that the posterior distribution contracts around the true $\\theta$ at (near) minimax rate under very mild conditions. In the proce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04369","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}