{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JHFZVS4GOPA2QUTFH3OVR4OHJO","short_pith_number":"pith:JHFZVS4G","canonical_record":{"source":{"id":"1311.1454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-11-06T17:34:08Z","cross_cats_sorted":["math.ST","stat.AP","stat.TH"],"title_canon_sha256":"08555ffb4d1b232851efb4bce86c27d8a9a30ee3120a3adccd1822db18387c84","abstract_canon_sha256":"98d00a19d59ea473374433201dea0dfdcbf29072abbf8a5f9214053db237f13a"},"schema_version":"1.0"},"canonical_sha256":"49cb9acb8673c1a852653edd58f1c74b9e621b963f105d34d7f2bbadb1f8061c","source":{"kind":"arxiv","id":"1311.1454","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1454","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1454v2","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1454","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"pith_short_12","alias_value":"JHFZVS4GOPA2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JHFZVS4GOPA2QUTF","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JHFZVS4G","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JHFZVS4GOPA2QUTFH3OVR4OHJO","target":"record","payload":{"canonical_record":{"source":{"id":"1311.1454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-11-06T17:34:08Z","cross_cats_sorted":["math.ST","stat.AP","stat.TH"],"title_canon_sha256":"08555ffb4d1b232851efb4bce86c27d8a9a30ee3120a3adccd1822db18387c84","abstract_canon_sha256":"98d00a19d59ea473374433201dea0dfdcbf29072abbf8a5f9214053db237f13a"},"schema_version":"1.0"},"canonical_sha256":"49cb9acb8673c1a852653edd58f1c74b9e621b963f105d34d7f2bbadb1f8061c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:42.015968Z","signature_b64":"iiVHxdszirmyw+x2TZnASYE7olaaIk8zEC5m8kx4DXp4pXySW5LDWqz9DKhWvNwk0Uf8+Ee3twAmspj7/4FbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49cb9acb8673c1a852653edd58f1c74b9e621b963f105d34d7f2bbadb1f8061c","last_reissued_at":"2026-05-18T03:07:42.015211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:42.015211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.1454","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o4iYHR9/deIHj8N2sHEWK1qRH90fZqGZRSM9mp+2HnFNTYR7AGGjI4bnSkc3aPTFYDps5JDSB3xU81J8fNK7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:21:37.221923Z"},"content_sha256":"f3a383c13f2bb19f069dcebef1db864cfa36e3e682957633aea5ef0bca3364af","schema_version":"1.0","event_id":"sha256:f3a383c13f2bb19f069dcebef1db864cfa36e3e682957633aea5ef0bca3364af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JHFZVS4GOPA2QUTFH3OVR4OHJO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On posterior propriety for the Student-$t$ linear regression model under Jeffreys priors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.AP","stat.TH"],"primary_cat":"stat.ME","authors_text":"Catalina A. Vallejos, Mark F.J. Steel","submitted_at":"2013-11-06T17:34:08Z","abstract_excerpt":"Regression models with fat-tailed error terms are an increasingly popular choice to obtain more robust inference to the presence of outlying observations. This article focuses on Bayesian inference for the Student-$t$ linear regression model under objective priors that are based on the Jeffreys rule. Posterior propriety results presented in Fonseca et al. (2008) are revisited and corrected. In particular, it is shown that the standard Jeffreys-rule prior precludes the existence of a proper posterior distribution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1454","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZzIBwDhCNgiNCIwK8QuBfUwt2K4YzBb6pgDwtZRbtVeBfBjHvTGs8QVYJk/Qd4HhUMHtB8Vd6+T6TPxlQsCBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:21:37.222274Z"},"content_sha256":"c02ee1b8bc42ae522338125f1dc217a66d144d5f14fbff77414b427b33da7c36","schema_version":"1.0","event_id":"sha256:c02ee1b8bc42ae522338125f1dc217a66d144d5f14fbff77414b427b33da7c36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JHFZVS4GOPA2QUTFH3OVR4OHJO/bundle.json","state_url":"https://pith.science/pith/JHFZVS4GOPA2QUTFH3OVR4OHJO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JHFZVS4GOPA2QUTFH3OVR4OHJO/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":"2026-06-21T22:21:37Z","links":{"resolver":"https://pith.science/pith/JHFZVS4GOPA2QUTFH3OVR4OHJO","bundle":"https://pith.science/pith/JHFZVS4GOPA2QUTFH3OVR4OHJO/bundle.json","state":"https://pith.science/pith/JHFZVS4GOPA2QUTFH3OVR4OHJO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JHFZVS4GOPA2QUTFH3OVR4OHJO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JHFZVS4GOPA2QUTFH3OVR4OHJO","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":"98d00a19d59ea473374433201dea0dfdcbf29072abbf8a5f9214053db237f13a","cross_cats_sorted":["math.ST","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-11-06T17:34:08Z","title_canon_sha256":"08555ffb4d1b232851efb4bce86c27d8a9a30ee3120a3adccd1822db18387c84"},"schema_version":"1.0","source":{"id":"1311.1454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1454","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1454v2","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1454","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"pith_short_12","alias_value":"JHFZVS4GOPA2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JHFZVS4GOPA2QUTF","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JHFZVS4G","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:c02ee1b8bc42ae522338125f1dc217a66d144d5f14fbff77414b427b33da7c36","target":"graph","created_at":"2026-05-18T03:07:42Z","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":"Regression models with fat-tailed error terms are an increasingly popular choice to obtain more robust inference to the presence of outlying observations. This article focuses on Bayesian inference for the Student-$t$ linear regression model under objective priors that are based on the Jeffreys rule. Posterior propriety results presented in Fonseca et al. (2008) are revisited and corrected. In particular, it is shown that the standard Jeffreys-rule prior precludes the existence of a proper posterior distribution.","authors_text":"Catalina A. Vallejos, Mark F.J. Steel","cross_cats":["math.ST","stat.AP","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-11-06T17:34:08Z","title":"On posterior propriety for the Student-$t$ linear regression model under Jeffreys priors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1454","kind":"arxiv","version":2},"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:f3a383c13f2bb19f069dcebef1db864cfa36e3e682957633aea5ef0bca3364af","target":"record","created_at":"2026-05-18T03:07:42Z","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":"98d00a19d59ea473374433201dea0dfdcbf29072abbf8a5f9214053db237f13a","cross_cats_sorted":["math.ST","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-11-06T17:34:08Z","title_canon_sha256":"08555ffb4d1b232851efb4bce86c27d8a9a30ee3120a3adccd1822db18387c84"},"schema_version":"1.0","source":{"id":"1311.1454","kind":"arxiv","version":2}},"canonical_sha256":"49cb9acb8673c1a852653edd58f1c74b9e621b963f105d34d7f2bbadb1f8061c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49cb9acb8673c1a852653edd58f1c74b9e621b963f105d34d7f2bbadb1f8061c","first_computed_at":"2026-05-18T03:07:42.015211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:42.015211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iiVHxdszirmyw+x2TZnASYE7olaaIk8zEC5m8kx4DXp4pXySW5LDWqz9DKhWvNwk0Uf8+Ee3twAmspj7/4FbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:42.015968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3a383c13f2bb19f069dcebef1db864cfa36e3e682957633aea5ef0bca3364af","sha256:c02ee1b8bc42ae522338125f1dc217a66d144d5f14fbff77414b427b33da7c36"],"state_sha256":"a995f416523acce604f02ec55284555c8291a0035981a14fc2a1b7bed52edbbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MsIjCaGglI6juK0y4+HNhhInoZh8VnoLIAvw5mSNNwMmeKGLArXhsXCOXAMC8wM4sodwmvhYfV3op4Zl7ZlPBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:21:37.224288Z","bundle_sha256":"ea2da910c577f38de8c1b789d2d624f3e678945f331b58730a1377c9a3ab71b3"}}