{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7K3655ZCDHXLZUFINVQWSRDZDI","short_pith_number":"pith:7K3655ZC","canonical_record":{"source":{"id":"1310.7479","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.ST","submitted_at":"2013-10-28T16:23:50Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"4a58142d560d9ec31cdf03a1204a3551d0ce140b007f83a1e66b6e5489d045b5","abstract_canon_sha256":"af60c9f32901c1d140e5b9b485d0b83f7a0f08f83a29549d251fa5e44e5f56f5"},"schema_version":"1.0"},"canonical_sha256":"fab7eef72219eebcd0a86d616944791a0bee3781aacba40338a46b4af851b52d","source":{"kind":"arxiv","id":"1310.7479","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7479","created_at":"2026-05-18T03:08:39Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7479v1","created_at":"2026-05-18T03:08:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7479","created_at":"2026-05-18T03:08:39Z"},{"alias_kind":"pith_short_12","alias_value":"7K3655ZCDHXL","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7K3655ZCDHXLZUFI","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7K3655ZC","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7K3655ZCDHXLZUFINVQWSRDZDI","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7479","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.ST","submitted_at":"2013-10-28T16:23:50Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"4a58142d560d9ec31cdf03a1204a3551d0ce140b007f83a1e66b6e5489d045b5","abstract_canon_sha256":"af60c9f32901c1d140e5b9b485d0b83f7a0f08f83a29549d251fa5e44e5f56f5"},"schema_version":"1.0"},"canonical_sha256":"fab7eef72219eebcd0a86d616944791a0bee3781aacba40338a46b4af851b52d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:39.010359Z","signature_b64":"WeuJNRoYNyj2Wl3pZJKvgvpO1Vy6ajUOeQyK9SDexok90CpuYgXJXgnSgc/XC84SCrl1SG6vbgouAadK+ncZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fab7eef72219eebcd0a86d616944791a0bee3781aacba40338a46b4af851b52d","last_reissued_at":"2026-05-18T03:08:39.009924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:39.009924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7479","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aQ3THYCSKtmNioicalQcuYMChK3wTXEfgXWP8dI0DO6uHxoZfkpyEljhM8N0Z3YkGZAF7fwDbXAqVsmNfyFXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:57:37.269764Z"},"content_sha256":"e2adf1152201bd200ec36cf39ba58e4041326443f42a963fcf917a318bbae897","schema_version":"1.0","event_id":"sha256:e2adf1152201bd200ec36cf39ba58e4041326443f42a963fcf917a318bbae897"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7K3655ZCDHXLZUFINVQWSRDZDI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak Convergence Rates of Population versus Single-Chain Stochastic Approximation MCMC Algorithms","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Faming Liang, Mingqi Wu, Qifan Song","submitted_at":"2013-10-28T16:23:50Z","abstract_excerpt":"In this paper, we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation MCMC algorithms. Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1/t), where t indexes the number of iterations. This is of interest for practica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7479","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s7MvuR0WF1AzYFP+4rsAFRst0CsxAjU9gHqkOmkaHV3okXy0oYYnm6t1gGVubMZnpv9n2PLh98B/Vfn0cY9oDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:57:37.270111Z"},"content_sha256":"8e21f94921136d690c1926bf11990df91d336446a326c4a2674e9571f190119d","schema_version":"1.0","event_id":"sha256:8e21f94921136d690c1926bf11990df91d336446a326c4a2674e9571f190119d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7K3655ZCDHXLZUFINVQWSRDZDI/bundle.json","state_url":"https://pith.science/pith/7K3655ZCDHXLZUFINVQWSRDZDI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7K3655ZCDHXLZUFINVQWSRDZDI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T08:57:37Z","links":{"resolver":"https://pith.science/pith/7K3655ZCDHXLZUFINVQWSRDZDI","bundle":"https://pith.science/pith/7K3655ZCDHXLZUFINVQWSRDZDI/bundle.json","state":"https://pith.science/pith/7K3655ZCDHXLZUFINVQWSRDZDI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7K3655ZCDHXLZUFINVQWSRDZDI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7K3655ZCDHXLZUFINVQWSRDZDI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"af60c9f32901c1d140e5b9b485d0b83f7a0f08f83a29549d251fa5e44e5f56f5","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.ST","submitted_at":"2013-10-28T16:23:50Z","title_canon_sha256":"4a58142d560d9ec31cdf03a1204a3551d0ce140b007f83a1e66b6e5489d045b5"},"schema_version":"1.0","source":{"id":"1310.7479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7479","created_at":"2026-05-18T03:08:39Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7479v1","created_at":"2026-05-18T03:08:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7479","created_at":"2026-05-18T03:08:39Z"},{"alias_kind":"pith_short_12","alias_value":"7K3655ZCDHXL","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7K3655ZCDHXLZUFI","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7K3655ZC","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:8e21f94921136d690c1926bf11990df91d336446a326c4a2674e9571f190119d","target":"graph","created_at":"2026-05-18T03:08:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation MCMC algorithms. Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1/t), where t indexes the number of iterations. This is of interest for practica","authors_text":"Faming Liang, Mingqi Wu, Qifan Song","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.ST","submitted_at":"2013-10-28T16:23:50Z","title":"Weak Convergence Rates of Population versus Single-Chain Stochastic Approximation MCMC Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7479","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e2adf1152201bd200ec36cf39ba58e4041326443f42a963fcf917a318bbae897","target":"record","created_at":"2026-05-18T03:08:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"af60c9f32901c1d140e5b9b485d0b83f7a0f08f83a29549d251fa5e44e5f56f5","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.ST","submitted_at":"2013-10-28T16:23:50Z","title_canon_sha256":"4a58142d560d9ec31cdf03a1204a3551d0ce140b007f83a1e66b6e5489d045b5"},"schema_version":"1.0","source":{"id":"1310.7479","kind":"arxiv","version":1}},"canonical_sha256":"fab7eef72219eebcd0a86d616944791a0bee3781aacba40338a46b4af851b52d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fab7eef72219eebcd0a86d616944791a0bee3781aacba40338a46b4af851b52d","first_computed_at":"2026-05-18T03:08:39.009924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:39.009924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WeuJNRoYNyj2Wl3pZJKvgvpO1Vy6ajUOeQyK9SDexok90CpuYgXJXgnSgc/XC84SCrl1SG6vbgouAadK+ncZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:39.010359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2adf1152201bd200ec36cf39ba58e4041326443f42a963fcf917a318bbae897","sha256:8e21f94921136d690c1926bf11990df91d336446a326c4a2674e9571f190119d"],"state_sha256":"e47055c05d9a53e0ccfdc4a62d3d01dd8117fc607933d3586a78e63016dfea78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W6rdcd2ZXKHOfXgMZoEfzBUVy+oaP0tJbHzJYZJPXuh0mF3mBpLr9sa4jq8dQMa+iJcY5qG107XAE1JxZeWzCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:57:37.272063Z","bundle_sha256":"4d536ce65d267e6db7d8d08cdac567bffddf3c11042c973165a78e7f789da2d0"}}