{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:SMVYFCMEA3CZHXTHNQTMSCBULE","short_pith_number":"pith:SMVYFCME","schema_version":"1.0","canonical_sha256":"932b82898406c593de676c26c90834593dfbdec1b64fcceb658aef3e12320b57","source":{"kind":"arxiv","id":"1206.4770","version":1},"attestation_state":"computed","paper":{"title":"On the Geometric Ergodicity of Two-Variable Gibbs Samplers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Aixin Tan, Galin L. Jones, James P. Hobert","submitted_at":"2012-06-21T03:19:20Z","abstract_excerpt":"A Markov chain is geometrically ergodic if it converges to its in- variant distribution at a geometric rate in total variation norm. We study geo- metric ergodicity of deterministic and random scan versions of the two-variable Gibbs sampler. We give a sufficient condition which simultaneously guarantees both versions are geometrically ergodic. We also develop a method for simul- taneously establishing that both versions are subgeometrically ergodic. These general results allow us to characterize the convergence rate of two-variable Gibbs samplers in a particular family of discrete bivariate di"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1206.4770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-06-21T03:19:20Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c79531415a6cf9f97ee19c790ed2a4018bfff06231a110942c2f35fdeb2cd4e8","abstract_canon_sha256":"1cec3b713278509daba0298d1a994b41edeed80aaf7990430e74d2d1b0f15031"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:03.757221Z","signature_b64":"910Qf3KiyYom9bnT0EtbNUSqlXR/ndqnU/gVpfpld9SggFoZXg1q2+L1XndZ+smuRxfVIMV5e1H/VDy+wOozBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"932b82898406c593de676c26c90834593dfbdec1b64fcceb658aef3e12320b57","last_reissued_at":"2026-05-18T03:53:03.756514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:03.756514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Geometric Ergodicity of Two-Variable Gibbs Samplers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Aixin Tan, Galin L. Jones, James P. Hobert","submitted_at":"2012-06-21T03:19:20Z","abstract_excerpt":"A Markov chain is geometrically ergodic if it converges to its in- variant distribution at a geometric rate in total variation norm. We study geo- metric ergodicity of deterministic and random scan versions of the two-variable Gibbs sampler. We give a sufficient condition which simultaneously guarantees both versions are geometrically ergodic. We also develop a method for simul- taneously establishing that both versions are subgeometrically ergodic. These general results allow us to characterize the convergence rate of two-variable Gibbs samplers in a particular family of discrete bivariate di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4770","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1206.4770","created_at":"2026-05-18T03:53:03.756636+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.4770v1","created_at":"2026-05-18T03:53:03.756636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4770","created_at":"2026-05-18T03:53:03.756636+00:00"},{"alias_kind":"pith_short_12","alias_value":"SMVYFCMEA3CZ","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"SMVYFCMEA3CZHXTH","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"SMVYFCME","created_at":"2026-05-18T12:27:20.899486+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SMVYFCMEA3CZHXTHNQTMSCBULE","json":"https://pith.science/pith/SMVYFCMEA3CZHXTHNQTMSCBULE.json","graph_json":"https://pith.science/api/pith-number/SMVYFCMEA3CZHXTHNQTMSCBULE/graph.json","events_json":"https://pith.science/api/pith-number/SMVYFCMEA3CZHXTHNQTMSCBULE/events.json","paper":"https://pith.science/paper/SMVYFCME"},"agent_actions":{"view_html":"https://pith.science/pith/SMVYFCMEA3CZHXTHNQTMSCBULE","download_json":"https://pith.science/pith/SMVYFCMEA3CZHXTHNQTMSCBULE.json","view_paper":"https://pith.science/paper/SMVYFCME","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.4770&json=true","fetch_graph":"https://pith.science/api/pith-number/SMVYFCMEA3CZHXTHNQTMSCBULE/graph.json","fetch_events":"https://pith.science/api/pith-number/SMVYFCMEA3CZHXTHNQTMSCBULE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SMVYFCMEA3CZHXTHNQTMSCBULE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SMVYFCMEA3CZHXTHNQTMSCBULE/action/storage_attestation","attest_author":"https://pith.science/pith/SMVYFCMEA3CZHXTHNQTMSCBULE/action/author_attestation","sign_citation":"https://pith.science/pith/SMVYFCMEA3CZHXTHNQTMSCBULE/action/citation_signature","submit_replication":"https://pith.science/pith/SMVYFCMEA3CZHXTHNQTMSCBULE/action/replication_record"}},"created_at":"2026-05-18T03:53:03.756636+00:00","updated_at":"2026-05-18T03:53:03.756636+00:00"}