{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MCCDG55GVASQZYUVBQIB275ORU","short_pith_number":"pith:MCCDG55G","canonical_record":{"source":{"id":"1511.00764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-11-03T03:37:40Z","cross_cats_sorted":[],"title_canon_sha256":"1a5a1c087ded3ead41afc5baceee63d73cc9c62cfb7e25003a8b6ec3cbe2b7d9","abstract_canon_sha256":"dabcb41e36d16571583abac19adb3c0fa8d8ee0520b97a4181d1a54a3f238e07"},"schema_version":"1.0"},"canonical_sha256":"60843377a6a8250ce2950c101d7fae8d0cfaba34c2881cf847ef993692e6542a","source":{"kind":"arxiv","id":"1511.00764","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00764","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00764v1","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00764","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"MCCDG55GVASQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MCCDG55GVASQZYUV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MCCDG55G","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MCCDG55GVASQZYUVBQIB275ORU","target":"record","payload":{"canonical_record":{"source":{"id":"1511.00764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-11-03T03:37:40Z","cross_cats_sorted":[],"title_canon_sha256":"1a5a1c087ded3ead41afc5baceee63d73cc9c62cfb7e25003a8b6ec3cbe2b7d9","abstract_canon_sha256":"dabcb41e36d16571583abac19adb3c0fa8d8ee0520b97a4181d1a54a3f238e07"},"schema_version":"1.0"},"canonical_sha256":"60843377a6a8250ce2950c101d7fae8d0cfaba34c2881cf847ef993692e6542a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:06.460643Z","signature_b64":"TzV6g8ZyqtJlqhjLHdYKSqSR2Sx/xyEM6+4BKPjOiAmREkcnwvUojwUETz/L5mkyoEIPIW7EGHvkBUN6xTIxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60843377a6a8250ce2950c101d7fae8d0cfaba34c2881cf847ef993692e6542a","last_reissued_at":"2026-05-18T01:28:06.460029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:06.460029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.00764","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":"2026-05-18T01:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"94Na4Wo869CTSg9/+zmlL5lW/aMjm1uaCM0yvx8T6gvDHOpTS3vPX27zY1+jWptMcjTBaB/PpqjE39ULwAy/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:46:38.170304Z"},"content_sha256":"290c1a072022187490c92d40d95d657276d0c641d7419199d395b74db24ac4fc","schema_version":"1.0","event_id":"sha256:290c1a072022187490c92d40d95d657276d0c641d7419199d395b74db24ac4fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MCCDG55GVASQZYUVBQIB275ORU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Gaussian approximations to the posterior for log-linear models with Diaconis-Ylvisaker priors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Anirban Bhattacharya, James E. Johndrow","submitted_at":"2015-11-03T03:37:40Z","abstract_excerpt":"In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis-Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. Here we derive the op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00764","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":"2026-05-18T01:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qrst3bw8I21hCtwnbDWGPoB+qJnTTJi9CjbvzDuq6TQ/NE9gmJQOSRdX3W8N25fpg/pRJLeLM95STtc08CFYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:46:38.171088Z"},"content_sha256":"d7b621616ffe366ebb3b3372f6866b8ae7efacb88e4278d7b4b29e5867725265","schema_version":"1.0","event_id":"sha256:d7b621616ffe366ebb3b3372f6866b8ae7efacb88e4278d7b4b29e5867725265"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MCCDG55GVASQZYUVBQIB275ORU/bundle.json","state_url":"https://pith.science/pith/MCCDG55GVASQZYUVBQIB275ORU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MCCDG55GVASQZYUVBQIB275ORU/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":"2026-05-25T15:46:38Z","links":{"resolver":"https://pith.science/pith/MCCDG55GVASQZYUVBQIB275ORU","bundle":"https://pith.science/pith/MCCDG55GVASQZYUVBQIB275ORU/bundle.json","state":"https://pith.science/pith/MCCDG55GVASQZYUVBQIB275ORU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MCCDG55GVASQZYUVBQIB275ORU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MCCDG55GVASQZYUVBQIB275ORU","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":"dabcb41e36d16571583abac19adb3c0fa8d8ee0520b97a4181d1a54a3f238e07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-11-03T03:37:40Z","title_canon_sha256":"1a5a1c087ded3ead41afc5baceee63d73cc9c62cfb7e25003a8b6ec3cbe2b7d9"},"schema_version":"1.0","source":{"id":"1511.00764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00764","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00764v1","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00764","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"MCCDG55GVASQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MCCDG55GVASQZYUV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MCCDG55G","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:d7b621616ffe366ebb3b3372f6866b8ae7efacb88e4278d7b4b29e5867725265","target":"graph","created_at":"2026-05-18T01:28:06Z","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 contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis-Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. Here we derive the op","authors_text":"Anirban Bhattacharya, James E. Johndrow","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-11-03T03:37:40Z","title":"Optimal Gaussian approximations to the posterior for log-linear models with Diaconis-Ylvisaker priors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00764","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":"sha256:290c1a072022187490c92d40d95d657276d0c641d7419199d395b74db24ac4fc","target":"record","created_at":"2026-05-18T01:28:06Z","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":"dabcb41e36d16571583abac19adb3c0fa8d8ee0520b97a4181d1a54a3f238e07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-11-03T03:37:40Z","title_canon_sha256":"1a5a1c087ded3ead41afc5baceee63d73cc9c62cfb7e25003a8b6ec3cbe2b7d9"},"schema_version":"1.0","source":{"id":"1511.00764","kind":"arxiv","version":1}},"canonical_sha256":"60843377a6a8250ce2950c101d7fae8d0cfaba34c2881cf847ef993692e6542a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60843377a6a8250ce2950c101d7fae8d0cfaba34c2881cf847ef993692e6542a","first_computed_at":"2026-05-18T01:28:06.460029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:06.460029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TzV6g8ZyqtJlqhjLHdYKSqSR2Sx/xyEM6+4BKPjOiAmREkcnwvUojwUETz/L5mkyoEIPIW7EGHvkBUN6xTIxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:06.460643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:290c1a072022187490c92d40d95d657276d0c641d7419199d395b74db24ac4fc","sha256:d7b621616ffe366ebb3b3372f6866b8ae7efacb88e4278d7b4b29e5867725265"],"state_sha256":"8fcbb72a587df27495feac347a58cf4a46bab6910873368d708d20b8b2f8f9d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JOayyhk1Ro38OR4RgdiBgabiNITCjYo6+ASWJFNFXtMTFYMZ6sGTxZeuNTE6E5v7/6nPXTMW7xtn9H6TB1SCBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:46:38.174931Z","bundle_sha256":"21ef28d1e7d655468f44690f525818c546573b12366a37752e30063cef608afc"}}