{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:I4Y2YRCRXADSY5FVM6ZFDZIJAW","short_pith_number":"pith:I4Y2YRCR","canonical_record":{"source":{"id":"0904.2144","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2009-04-14T15:38:16Z","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"title_canon_sha256":"a24a2778e3b49433122293ce7db375db2dc335d15688aa2f2c781495965cf8c1","abstract_canon_sha256":"f450f4efcabef7dcee75e8a53b3cef49565f96a34b12c60a99a64338f72af1bc"},"schema_version":"1.0"},"canonical_sha256":"4731ac4451b8072c74b567b251e509058c6d9820c6f29b90c7b2c53198f407a3","source":{"kind":"arxiv","id":"0904.2144","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2144","created_at":"2026-05-18T04:27:16Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2144v6","created_at":"2026-05-18T04:27:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2144","created_at":"2026-05-18T04:27:16Z"},{"alias_kind":"pith_short_12","alias_value":"I4Y2YRCRXADS","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"I4Y2YRCRXADSY5FV","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"I4Y2YRCR","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:I4Y2YRCRXADSY5FVM6ZFDZIJAW","target":"record","payload":{"canonical_record":{"source":{"id":"0904.2144","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2009-04-14T15:38:16Z","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"title_canon_sha256":"a24a2778e3b49433122293ce7db375db2dc335d15688aa2f2c781495965cf8c1","abstract_canon_sha256":"f450f4efcabef7dcee75e8a53b3cef49565f96a34b12c60a99a64338f72af1bc"},"schema_version":"1.0"},"canonical_sha256":"4731ac4451b8072c74b567b251e509058c6d9820c6f29b90c7b2c53198f407a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:16.454594Z","signature_b64":"cjeSGJYASQcVlFHmsrvZ+KypLsOF8OzohrbUgVGrlErE4mY7E9n2rIZNFKAIbeU5Bid8vHlAbxito6XUU3C5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4731ac4451b8072c74b567b251e509058c6d9820c6f29b90c7b2c53198f407a3","last_reissued_at":"2026-05-18T04:27:16.453901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:16.453901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.2144","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:27:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FdGd6XzhK3tuYlKaVScDqfaUm+axc7liJxn5hpaLK6kZ16h6eD6Sm2hz5B2LeYRt3VlRqGxgQv9jAsPVIHywAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:22:34.699679Z"},"content_sha256":"87c14e8cce0fbfc57e73ea6124cbf9b137545183fb60da6b98da5ec21e248f7b","schema_version":"1.0","event_id":"sha256:87c14e8cce0fbfc57e73ea6124cbf9b137545183fb60da6b98da5ec21e248f7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:I4Y2YRCRXADSY5FVM6ZFDZIJAW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A vanilla Rao--Blackwellization of Metropolis--Hastings algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.ME","stat.TH"],"primary_cat":"stat.CO","authors_text":"Christian P. Robert, Randal Douc","submitted_at":"2009-04-14T15:38:16Z","abstract_excerpt":"Casella and Robert [Biometrika 83 (1996) 81--94] presented a general Rao--Blackwellization principle for accept-reject and Metropolis--Hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at a high cost in computation and storage. Adopting a completely different perspective, we introduce instead a universal scheme that guarantees variance reductions in all Metropolis--Hastings-based estimators while keeping the computation cost under control. We establish a central limit theorem for the improved estimators and illustrate their performances on to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2144","kind":"arxiv","version":6},"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":"2026-05-18T04:27:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t02o05UFP3H2KoOK3AlTzwJ/AixoGbW9Wbl1RxPC6oZAlFncxpL8t6/Uvrfdw3OOi+i33qPzVmrtxC/ExNZhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:22:34.700348Z"},"content_sha256":"53910a6ee80404d2e26647584a55f4c371e379612aa69f8159ebd8fa75162c65","schema_version":"1.0","event_id":"sha256:53910a6ee80404d2e26647584a55f4c371e379612aa69f8159ebd8fa75162c65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4Y2YRCRXADSY5FVM6ZFDZIJAW/bundle.json","state_url":"https://pith.science/pith/I4Y2YRCRXADSY5FVM6ZFDZIJAW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4Y2YRCRXADSY5FVM6ZFDZIJAW/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":"2026-05-26T17:22:34Z","links":{"resolver":"https://pith.science/pith/I4Y2YRCRXADSY5FVM6ZFDZIJAW","bundle":"https://pith.science/pith/I4Y2YRCRXADSY5FVM6ZFDZIJAW/bundle.json","state":"https://pith.science/pith/I4Y2YRCRXADSY5FVM6ZFDZIJAW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4Y2YRCRXADSY5FVM6ZFDZIJAW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:I4Y2YRCRXADSY5FVM6ZFDZIJAW","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":"f450f4efcabef7dcee75e8a53b3cef49565f96a34b12c60a99a64338f72af1bc","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2009-04-14T15:38:16Z","title_canon_sha256":"a24a2778e3b49433122293ce7db375db2dc335d15688aa2f2c781495965cf8c1"},"schema_version":"1.0","source":{"id":"0904.2144","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2144","created_at":"2026-05-18T04:27:16Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2144v6","created_at":"2026-05-18T04:27:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2144","created_at":"2026-05-18T04:27:16Z"},{"alias_kind":"pith_short_12","alias_value":"I4Y2YRCRXADS","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"I4Y2YRCRXADSY5FV","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"I4Y2YRCR","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:53910a6ee80404d2e26647584a55f4c371e379612aa69f8159ebd8fa75162c65","target":"graph","created_at":"2026-05-18T04:27:16Z","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":"Casella and Robert [Biometrika 83 (1996) 81--94] presented a general Rao--Blackwellization principle for accept-reject and Metropolis--Hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at a high cost in computation and storage. Adopting a completely different perspective, we introduce instead a universal scheme that guarantees variance reductions in all Metropolis--Hastings-based estimators while keeping the computation cost under control. We establish a central limit theorem for the improved estimators and illustrate their performances on to","authors_text":"Christian P. Robert, Randal Douc","cross_cats":["math.ST","stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2009-04-14T15:38:16Z","title":"A vanilla Rao--Blackwellization of Metropolis--Hastings algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2144","kind":"arxiv","version":6},"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":"sha256:87c14e8cce0fbfc57e73ea6124cbf9b137545183fb60da6b98da5ec21e248f7b","target":"record","created_at":"2026-05-18T04:27:16Z","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":"f450f4efcabef7dcee75e8a53b3cef49565f96a34b12c60a99a64338f72af1bc","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2009-04-14T15:38:16Z","title_canon_sha256":"a24a2778e3b49433122293ce7db375db2dc335d15688aa2f2c781495965cf8c1"},"schema_version":"1.0","source":{"id":"0904.2144","kind":"arxiv","version":6}},"canonical_sha256":"4731ac4451b8072c74b567b251e509058c6d9820c6f29b90c7b2c53198f407a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4731ac4451b8072c74b567b251e509058c6d9820c6f29b90c7b2c53198f407a3","first_computed_at":"2026-05-18T04:27:16.453901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:16.453901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cjeSGJYASQcVlFHmsrvZ+KypLsOF8OzohrbUgVGrlErE4mY7E9n2rIZNFKAIbeU5Bid8vHlAbxito6XUU3C5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:16.454594Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2144","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87c14e8cce0fbfc57e73ea6124cbf9b137545183fb60da6b98da5ec21e248f7b","sha256:53910a6ee80404d2e26647584a55f4c371e379612aa69f8159ebd8fa75162c65"],"state_sha256":"38751e4cd48a4112c5d06b162e7c62bfe7b230150523ab70b887357141d3ed7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P2QeSp5dTG3D9VuZ9GEAfOAVTttls3l3Vc0SRvkXhgnVdPfTVBG97ZdWAHCXgPL0g3YC/iMvsR8ziNCqLSV/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T17:22:34.703655Z","bundle_sha256":"706ae64bc3ad0c00ab172258c8d85cb185f281754b6ba77c807cf5e038a3d64a"}}