{"paper":{"title":"Geometric Ergodicity & Scanning Strategies For Two-Component Gibbs Samplers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Alicia A. Johnson, Owen Burbank","submitted_at":"2012-09-27T16:52:03Z","abstract_excerpt":"In any Markov chain Monte Carlo analysis, rapid convergence of the chain to its target probability distribution is of practical and theoretical importance. A chain that converges at a geometric rate is geometrically ergodic. In this paper, we explore geometric ergodicity for two-component Gibbs samplers which, under a chosen scanning strategy, evolve by combining one-at-a-time updates of the two components. We compare convergence behaviors between and within three such strategies: composition, random sequence scan, and random scan. Our main results are twofold. First, we establish that if the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6283","kind":"arxiv","version":2},"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"}