{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TSOGHXH5GHL7NGG4MSFFN4FGFT","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":"6ab553d233075251a883f9dce88a6c1b8d3abf043f5db240934ccd2ffbb943b1","cross_cats_sorted":["astro-ph.IM","stat.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2021-11-24T19:00:01Z","title_canon_sha256":"32682d5a476d8cb1573e83da1548d7c8b1753de532bbf7f7182a80e1c60a565e"},"schema_version":"1.0","source":{"id":"2111.12720","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.12720","created_at":"2026-07-05T07:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"2111.12720v3","created_at":"2026-07-05T07:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.12720","created_at":"2026-07-05T07:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"TSOGHXH5GHL7","created_at":"2026-07-05T07:15:43Z"},{"alias_kind":"pith_short_16","alias_value":"TSOGHXH5GHL7NGG4","created_at":"2026-07-05T07:15:43Z"},{"alias_kind":"pith_short_8","alias_value":"TSOGHXH5","created_at":"2026-07-05T07:15:43Z"}],"graph_snapshots":[{"event_id":"sha256:fcb1acdb013f8333c19410f10bc66f874e401cda3486b155d4b4dbe6652cccdf","target":"graph","created_at":"2026-07-05T07:15:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.12720/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We resurrect the infamous harmonic mean estimator for computing the marginal likelihood (Bayesian evidence) and solve its problematic large variance. The marginal likelihood is a key component of Bayesian model selection to evaluate model posterior probabilities; however, its computation is challenging. The original harmonic mean estimator, first proposed by Newton and Raftery in 1994, involves computing the harmonic mean of the likelihood given samples from the posterior. It was immediately realised that the original estimator can fail catastrophically since its variance can become very large","authors_text":"Alessio Spurio Mancini, Christopher G. R. Wallis, Jason D. McEwen, Matthew A. Price","cross_cats":["astro-ph.IM","stat.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2021-11-24T19:00:01Z","title":"Machine learning assisted Bayesian model comparison: learnt harmonic mean estimator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.12720","kind":"arxiv","version":3},"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":"sha256:16c08a646117088338f5e47a85364d6f8adc3a2efd5cb9ac2ad43065e9d092a3","target":"record","created_at":"2026-07-05T07:15:43Z","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":"6ab553d233075251a883f9dce88a6c1b8d3abf043f5db240934ccd2ffbb943b1","cross_cats_sorted":["astro-ph.IM","stat.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2021-11-24T19:00:01Z","title_canon_sha256":"32682d5a476d8cb1573e83da1548d7c8b1753de532bbf7f7182a80e1c60a565e"},"schema_version":"1.0","source":{"id":"2111.12720","kind":"arxiv","version":3}},"canonical_sha256":"9c9c63dcfd31d7f698dc648a56f0a62cdda49e90accb5318ccb8a658c105d60c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c9c63dcfd31d7f698dc648a56f0a62cdda49e90accb5318ccb8a658c105d60c","first_computed_at":"2026-07-05T07:15:43.092058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:15:43.092058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/U+Vf+cK6e6j20lYeIm2ZQZ8oBd17vNNLDuIPPRYDUtQrqUUig+HciL5Uy0kWO3AWAyP5Hc+BCUacfgyfMmRCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:15:43.092598Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.12720","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16c08a646117088338f5e47a85364d6f8adc3a2efd5cb9ac2ad43065e9d092a3","sha256:fcb1acdb013f8333c19410f10bc66f874e401cda3486b155d4b4dbe6652cccdf"],"state_sha256":"b162dcc899651c0ebbeacabcbd3d7c3b8fd5a779d887a64ae1b559e2e2306832"}