{"paper":{"title":"Finite sample posterior concentration in high-dimensional regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Artin Armagan, David Dunson, Lawrence Carin, Nate Strawn, Rayan Saab","submitted_at":"2012-07-20T05:52:24Z","abstract_excerpt":"We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite sample bounds ensuring sufficient posterior probability assigned in neighborhoods of the true regression coefficient vector, $\\beta^0$, with high probability. We assume that $\\beta^0$ is approximately $S$-sparse and obtain universal bounds, which provide insight into the role of the prior in controlling concentration of the posterior. Based on these finite samp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4854","kind":"arxiv","version":3},"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"}