{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OXJEA3AX5VDWM4ECBFEWOBHOLH","short_pith_number":"pith:OXJEA3AX","canonical_record":{"source":{"id":"1109.4180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-09-19T22:04:04Z","cross_cats_sorted":["math.ST","stat.CO","stat.TH"],"title_canon_sha256":"fd6852b16aa16bd511d720e302e0cdb59ef02ebd442722f0847c63516a0ad24b","abstract_canon_sha256":"30fa9acaa1691062bcff36a03fc5dec6370f38ef0b10227796eaa2eb7e6ec59b"},"schema_version":"1.0"},"canonical_sha256":"75d2406c17ed4766708209496704ee59d24f84384398e56f29f57be179af02b5","source":{"kind":"arxiv","id":"1109.4180","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4180","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4180v1","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4180","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"OXJEA3AX5VDW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OXJEA3AX5VDWM4EC","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OXJEA3AX","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OXJEA3AX5VDWM4ECBFEWOBHOLH","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-09-19T22:04:04Z","cross_cats_sorted":["math.ST","stat.CO","stat.TH"],"title_canon_sha256":"fd6852b16aa16bd511d720e302e0cdb59ef02ebd442722f0847c63516a0ad24b","abstract_canon_sha256":"30fa9acaa1691062bcff36a03fc5dec6370f38ef0b10227796eaa2eb7e6ec59b"},"schema_version":"1.0"},"canonical_sha256":"75d2406c17ed4766708209496704ee59d24f84384398e56f29f57be179af02b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:44.055266Z","signature_b64":"puQSC548gmwzUREZe/IXAyzd5njuDksFuVai3oHKCC2MMCIyNPgUh/c8TtC6WUsdzcvOxc070qB5i/b0gE1JAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75d2406c17ed4766708209496704ee59d24f84384398e56f29f57be179af02b5","last_reissued_at":"2026-05-18T04:12:44.054678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:44.054678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4180","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":"2026-05-18T04:12:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vArbVRUxOVO7ZgSq9r7/1o7lm+NbFdIAu+y/bt5dma6RpJjSV0ornHzFPeTj4FjHqKLZwJeqyyODTHmKY47Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T23:10:46.476692Z"},"content_sha256":"846c72d9848a4a7e9ec73405ca4aab49a62ee4505071972d35384dc6df875f05","schema_version":"1.0","event_id":"sha256:846c72d9848a4a7e9ec73405ca4aab49a62ee4505071972d35384dc6df875f05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OXJEA3AX5VDWM4ECBFEWOBHOLH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Default Bayesian analysis for multi-way tables: a data-augmentation approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.CO","stat.TH"],"primary_cat":"stat.ME","authors_text":"James G. Scott, Nicholas G. Polson","submitted_at":"2011-09-19T22:04:04Z","abstract_excerpt":"This paper proposes a strategy for regularized estimation in multi-way contingency tables, which are common in meta-analyses and multi-center clinical trials. Our approach is based on data augmentation, and appeals heavily to a novel class of Polya-Gamma distributions. Our main contributions are to build up the relevant distributional theory and to demonstrate three useful features of this data-augmentation scheme. First, it leads to simple EM and Gibbs-sampling algorithms for posterior inference, circumventing the need for analytic approximations, numerical integration, Metropolis--Hastings, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4180","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":"2026-05-18T04:12:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDiNSspqQtbbNzNg5Wv2m68GIo+axY/7X49cpYZqrSbtuqdCZbmuypbobi/zeWpLeDedgBjFz98PkJhZtDgaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T23:10:46.477359Z"},"content_sha256":"9bcdc0d2f38b107cead4637fc8acc559db90d37ae541a311e43468e99667a5f2","schema_version":"1.0","event_id":"sha256:9bcdc0d2f38b107cead4637fc8acc559db90d37ae541a311e43468e99667a5f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OXJEA3AX5VDWM4ECBFEWOBHOLH/bundle.json","state_url":"https://pith.science/pith/OXJEA3AX5VDWM4ECBFEWOBHOLH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OXJEA3AX5VDWM4ECBFEWOBHOLH/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":"2026-06-09T23:10:46Z","links":{"resolver":"https://pith.science/pith/OXJEA3AX5VDWM4ECBFEWOBHOLH","bundle":"https://pith.science/pith/OXJEA3AX5VDWM4ECBFEWOBHOLH/bundle.json","state":"https://pith.science/pith/OXJEA3AX5VDWM4ECBFEWOBHOLH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OXJEA3AX5VDWM4ECBFEWOBHOLH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OXJEA3AX5VDWM4ECBFEWOBHOLH","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":"30fa9acaa1691062bcff36a03fc5dec6370f38ef0b10227796eaa2eb7e6ec59b","cross_cats_sorted":["math.ST","stat.CO","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-09-19T22:04:04Z","title_canon_sha256":"fd6852b16aa16bd511d720e302e0cdb59ef02ebd442722f0847c63516a0ad24b"},"schema_version":"1.0","source":{"id":"1109.4180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4180","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4180v1","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4180","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"OXJEA3AX5VDW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OXJEA3AX5VDWM4EC","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OXJEA3AX","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:9bcdc0d2f38b107cead4637fc8acc559db90d37ae541a311e43468e99667a5f2","target":"graph","created_at":"2026-05-18T04:12:44Z","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":"This paper proposes a strategy for regularized estimation in multi-way contingency tables, which are common in meta-analyses and multi-center clinical trials. Our approach is based on data augmentation, and appeals heavily to a novel class of Polya-Gamma distributions. Our main contributions are to build up the relevant distributional theory and to demonstrate three useful features of this data-augmentation scheme. First, it leads to simple EM and Gibbs-sampling algorithms for posterior inference, circumventing the need for analytic approximations, numerical integration, Metropolis--Hastings, ","authors_text":"James G. Scott, Nicholas G. Polson","cross_cats":["math.ST","stat.CO","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-09-19T22:04:04Z","title":"Default Bayesian analysis for multi-way tables: a data-augmentation approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4180","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":"sha256:846c72d9848a4a7e9ec73405ca4aab49a62ee4505071972d35384dc6df875f05","target":"record","created_at":"2026-05-18T04:12:44Z","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":"30fa9acaa1691062bcff36a03fc5dec6370f38ef0b10227796eaa2eb7e6ec59b","cross_cats_sorted":["math.ST","stat.CO","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-09-19T22:04:04Z","title_canon_sha256":"fd6852b16aa16bd511d720e302e0cdb59ef02ebd442722f0847c63516a0ad24b"},"schema_version":"1.0","source":{"id":"1109.4180","kind":"arxiv","version":1}},"canonical_sha256":"75d2406c17ed4766708209496704ee59d24f84384398e56f29f57be179af02b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75d2406c17ed4766708209496704ee59d24f84384398e56f29f57be179af02b5","first_computed_at":"2026-05-18T04:12:44.054678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:44.054678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"puQSC548gmwzUREZe/IXAyzd5njuDksFuVai3oHKCC2MMCIyNPgUh/c8TtC6WUsdzcvOxc070qB5i/b0gE1JAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:44.055266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:846c72d9848a4a7e9ec73405ca4aab49a62ee4505071972d35384dc6df875f05","sha256:9bcdc0d2f38b107cead4637fc8acc559db90d37ae541a311e43468e99667a5f2"],"state_sha256":"458230d1dc6259d6b482a8e1b242b203a1d8064b25a5932b7ce755f2424e7002"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UDFD9GEvdazornJr6uxwo9lBv/xidZRJKOqR9OzGoFhpX1lJkvFWy2x5Yh0uAHdAQMWE+VuZdSh7wYRuemFdDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T23:10:46.481385Z","bundle_sha256":"c75c1832b1e1d54f2abd589f7e9c1d25afe6bcbfda4b417d56a7a8b7fed21359"}}