{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:6U3KQI646KLBFRQDFAOMUEOH2B","short_pith_number":"pith:6U3KQI64","schema_version":"1.0","canonical_sha256":"f536a823dcf29612c603281cca11c7d06579c916dcd144171562c07ec2eee24f","source":{"kind":"arxiv","id":"0910.1452","version":6},"attestation_state":"computed","paper":{"title":"On resolving the Savage-Dickey paradox","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Christian Robert, Jean-Michel Marin","submitted_at":"2009-10-08T09:34:37Z","abstract_excerpt":"The Savage-Dickey ratio is known as a specialised representation of the Bayes factor (O'Hagan and Forster, 2004) that allows for a functional plugging approximation of this quantity. We demonstrate here that the Savage-Dickey representation is in fact a generic representation of the Bayes factor that relies on specific measure-theoretic versions of the densities involved in the ratio, instead of a special identity imposing the above constraints on the prior distributions. We completely clarify the measure-theoretic foundations of the representation as well as the generalisation of Verdinelli a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0910.1452","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-10-08T09:34:37Z","cross_cats_sorted":["math.PR","stat.CO","stat.TH"],"title_canon_sha256":"047fc861d2a52f1700ecf3f403014fb499d3a352b3b2aa098bb8a95457e89c37","abstract_canon_sha256":"2433f35db33bca9d49a01b68f22c4148c637e1ae6c38310aa07ea110c1bb60ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:40.544679Z","signature_b64":"75q9g7PYhmTQfnihNYmUPzDUba3kD0cxkygM0pd/FZCxVyh2baoJ5Y0xkyM0aoDX4MilW10kDYeThKU4GZcvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f536a823dcf29612c603281cca11c7d06579c916dcd144171562c07ec2eee24f","last_reissued_at":"2026-05-18T04:39:40.544143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:40.544143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On resolving the Savage-Dickey paradox","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Christian Robert, Jean-Michel Marin","submitted_at":"2009-10-08T09:34:37Z","abstract_excerpt":"The Savage-Dickey ratio is known as a specialised representation of the Bayes factor (O'Hagan and Forster, 2004) that allows for a functional plugging approximation of this quantity. We demonstrate here that the Savage-Dickey representation is in fact a generic representation of the Bayes factor that relies on specific measure-theoretic versions of the densities involved in the ratio, instead of a special identity imposing the above constraints on the prior distributions. We completely clarify the measure-theoretic foundations of the representation as well as the generalisation of Verdinelli a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1452","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0910.1452","created_at":"2026-05-18T04:39:40.544215+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.1452v6","created_at":"2026-05-18T04:39:40.544215+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1452","created_at":"2026-05-18T04:39:40.544215+00:00"},{"alias_kind":"pith_short_12","alias_value":"6U3KQI646KLB","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"6U3KQI646KLBFRQD","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"6U3KQI64","created_at":"2026-05-18T12:25:58.837520+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.04339","citing_title":"Savage-Dickey density ratio estimation with normalizing flows for Bayesian model comparison","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6U3KQI646KLBFRQDFAOMUEOH2B","json":"https://pith.science/pith/6U3KQI646KLBFRQDFAOMUEOH2B.json","graph_json":"https://pith.science/api/pith-number/6U3KQI646KLBFRQDFAOMUEOH2B/graph.json","events_json":"https://pith.science/api/pith-number/6U3KQI646KLBFRQDFAOMUEOH2B/events.json","paper":"https://pith.science/paper/6U3KQI64"},"agent_actions":{"view_html":"https://pith.science/pith/6U3KQI646KLBFRQDFAOMUEOH2B","download_json":"https://pith.science/pith/6U3KQI646KLBFRQDFAOMUEOH2B.json","view_paper":"https://pith.science/paper/6U3KQI64","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.1452&json=true","fetch_graph":"https://pith.science/api/pith-number/6U3KQI646KLBFRQDFAOMUEOH2B/graph.json","fetch_events":"https://pith.science/api/pith-number/6U3KQI646KLBFRQDFAOMUEOH2B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6U3KQI646KLBFRQDFAOMUEOH2B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6U3KQI646KLBFRQDFAOMUEOH2B/action/storage_attestation","attest_author":"https://pith.science/pith/6U3KQI646KLBFRQDFAOMUEOH2B/action/author_attestation","sign_citation":"https://pith.science/pith/6U3KQI646KLBFRQDFAOMUEOH2B/action/citation_signature","submit_replication":"https://pith.science/pith/6U3KQI646KLBFRQDFAOMUEOH2B/action/replication_record"}},"created_at":"2026-05-18T04:39:40.544215+00:00","updated_at":"2026-05-18T04:39:40.544215+00:00"}