{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:TLVLN5YELFGAJAGWO2TB4YT75P","short_pith_number":"pith:TLVLN5YE","schema_version":"1.0","canonical_sha256":"9aeab6f704594c0480d676a61e627febea5a3d5c4eb9a1b13862dbd22d09ca24","source":{"kind":"arxiv","id":"1312.6432","version":2},"attestation_state":"computed","paper":{"title":"Uniform Ergodicity of the Iterated Conditional SMC and Geometric Ergodicity of Particle Gibbs samplers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anthony Lee, Christophe Andrieu, Matti Vihola","submitted_at":"2013-12-22T22:13:53Z","abstract_excerpt":"We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential boundedness of potential functions associated with the i-cSMC algorithm provide necessary and sufficient conditions for the uniform ergodicity of the i-cSMC Markov chain, as well as quantitative bounds on its (uniformly geometric) rate of convergence. Furthermore, we show that the i-cSMC Markov chain cannot even be geometrically ergodic if this essential boundedn"},"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":"1312.6432","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-22T22:13:53Z","cross_cats_sorted":[],"title_canon_sha256":"6bf9115604b47efec5af83170bab587b270e49e9f0c0832fd102bb5d418b4a56","abstract_canon_sha256":"19206775478f14a5761dac89777a2608943ab4170ceba3e6e35a12a8c168263f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:51.942912Z","signature_b64":"uu/GOK/Znbizrz0FYRmFNJZgdzXQVWZ/wJ3xtWvIJIzwTcFV1B+0rpGNdPcN6g1/KYNLV8I9VSTTq4Ux8k5ODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aeab6f704594c0480d676a61e627febea5a3d5c4eb9a1b13862dbd22d09ca24","last_reissued_at":"2026-05-18T02:18:51.942269Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:51.942269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform Ergodicity of the Iterated Conditional SMC and Geometric Ergodicity of Particle Gibbs samplers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anthony Lee, Christophe Andrieu, Matti Vihola","submitted_at":"2013-12-22T22:13:53Z","abstract_excerpt":"We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential boundedness of potential functions associated with the i-cSMC algorithm provide necessary and sufficient conditions for the uniform ergodicity of the i-cSMC Markov chain, as well as quantitative bounds on its (uniformly geometric) rate of convergence. Furthermore, we show that the i-cSMC Markov chain cannot even be geometrically ergodic if this essential boundedn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6432","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1312.6432","created_at":"2026-05-18T02:18:51.942414+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.6432v2","created_at":"2026-05-18T02:18:51.942414+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6432","created_at":"2026-05-18T02:18:51.942414+00:00"},{"alias_kind":"pith_short_12","alias_value":"TLVLN5YELFGA","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"TLVLN5YELFGAJAGW","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"TLVLN5YE","created_at":"2026-05-18T12:28:02.375192+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/TLVLN5YELFGAJAGWO2TB4YT75P","json":"https://pith.science/pith/TLVLN5YELFGAJAGWO2TB4YT75P.json","graph_json":"https://pith.science/api/pith-number/TLVLN5YELFGAJAGWO2TB4YT75P/graph.json","events_json":"https://pith.science/api/pith-number/TLVLN5YELFGAJAGWO2TB4YT75P/events.json","paper":"https://pith.science/paper/TLVLN5YE"},"agent_actions":{"view_html":"https://pith.science/pith/TLVLN5YELFGAJAGWO2TB4YT75P","download_json":"https://pith.science/pith/TLVLN5YELFGAJAGWO2TB4YT75P.json","view_paper":"https://pith.science/paper/TLVLN5YE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.6432&json=true","fetch_graph":"https://pith.science/api/pith-number/TLVLN5YELFGAJAGWO2TB4YT75P/graph.json","fetch_events":"https://pith.science/api/pith-number/TLVLN5YELFGAJAGWO2TB4YT75P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TLVLN5YELFGAJAGWO2TB4YT75P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TLVLN5YELFGAJAGWO2TB4YT75P/action/storage_attestation","attest_author":"https://pith.science/pith/TLVLN5YELFGAJAGWO2TB4YT75P/action/author_attestation","sign_citation":"https://pith.science/pith/TLVLN5YELFGAJAGWO2TB4YT75P/action/citation_signature","submit_replication":"https://pith.science/pith/TLVLN5YELFGAJAGWO2TB4YT75P/action/replication_record"}},"created_at":"2026-05-18T02:18:51.942414+00:00","updated_at":"2026-05-18T02:18:51.942414+00:00"}