{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GJH5T5X2WYRCWYLVWXVJVSYN34","short_pith_number":"pith:GJH5T5X2","schema_version":"1.0","canonical_sha256":"324fd9f6fab6222b6175b5ea9acb0ddf18f6556ea5f1230eddb9589829e14369","source":{"kind":"arxiv","id":"1712.01793","version":4},"attestation_state":"computed","paper":{"title":"Posterior Integration on a Riemannian Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Alessandro Barp, Chris. J. Oates, Mark Girolami","submitted_at":"2017-12-05T18:15:39Z","abstract_excerpt":"The geodesic Markov chain Monte Carlo method and its variants enable computation of integrals with respect to a posterior supported on a manifold. However, for regular integrals, the convergence rate of the ergodic average will be sub-optimal. To fill this gap, this paper extends the efficient posterior integration method of Oates et al. (2017) to the case of a Riemannian manifold. In contrast to the original Euclidean case, no non-trivial boundary conditions are needed for a closed manifold. The method is assessed through simulation and deployed to compute posterior integrals for an Australia"},"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":"1712.01793","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-12-05T18:15:39Z","cross_cats_sorted":[],"title_canon_sha256":"c577e0f6608325828b0c20770526b7bca8afb1bca4ce262904cb0e131d2bd655","abstract_canon_sha256":"ca6dd872fbeaa59bba3b5abae91368e4adbcc527b7c4e8958017b6657e912c2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:24.836532Z","signature_b64":"b2vNAWgjIGzPDPFD11bThwN5X0ei/1gXc5k/sA1Wx3RS3wFU1fTwj1AdNIypuYy3otDnDRUnfC9Nkqpi354RDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"324fd9f6fab6222b6175b5ea9acb0ddf18f6556ea5f1230eddb9589829e14369","last_reissued_at":"2026-05-18T00:03:24.836026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:24.836026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Posterior Integration on a Riemannian Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Alessandro Barp, Chris. J. Oates, Mark Girolami","submitted_at":"2017-12-05T18:15:39Z","abstract_excerpt":"The geodesic Markov chain Monte Carlo method and its variants enable computation of integrals with respect to a posterior supported on a manifold. However, for regular integrals, the convergence rate of the ergodic average will be sub-optimal. To fill this gap, this paper extends the efficient posterior integration method of Oates et al. (2017) to the case of a Riemannian manifold. In contrast to the original Euclidean case, no non-trivial boundary conditions are needed for a closed manifold. The method is assessed through simulation and deployed to compute posterior integrals for an Australia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01793","kind":"arxiv","version":4},"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":"1712.01793","created_at":"2026-05-18T00:03:24.836101+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.01793v4","created_at":"2026-05-18T00:03:24.836101+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.01793","created_at":"2026-05-18T00:03:24.836101+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJH5T5X2WYRC","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJH5T5X2WYRCWYLV","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJH5T5X2","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GJH5T5X2WYRCWYLVWXVJVSYN34","json":"https://pith.science/pith/GJH5T5X2WYRCWYLVWXVJVSYN34.json","graph_json":"https://pith.science/api/pith-number/GJH5T5X2WYRCWYLVWXVJVSYN34/graph.json","events_json":"https://pith.science/api/pith-number/GJH5T5X2WYRCWYLVWXVJVSYN34/events.json","paper":"https://pith.science/paper/GJH5T5X2"},"agent_actions":{"view_html":"https://pith.science/pith/GJH5T5X2WYRCWYLVWXVJVSYN34","download_json":"https://pith.science/pith/GJH5T5X2WYRCWYLVWXVJVSYN34.json","view_paper":"https://pith.science/paper/GJH5T5X2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.01793&json=true","fetch_graph":"https://pith.science/api/pith-number/GJH5T5X2WYRCWYLVWXVJVSYN34/graph.json","fetch_events":"https://pith.science/api/pith-number/GJH5T5X2WYRCWYLVWXVJVSYN34/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJH5T5X2WYRCWYLVWXVJVSYN34/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJH5T5X2WYRCWYLVWXVJVSYN34/action/storage_attestation","attest_author":"https://pith.science/pith/GJH5T5X2WYRCWYLVWXVJVSYN34/action/author_attestation","sign_citation":"https://pith.science/pith/GJH5T5X2WYRCWYLVWXVJVSYN34/action/citation_signature","submit_replication":"https://pith.science/pith/GJH5T5X2WYRCWYLVWXVJVSYN34/action/replication_record"}},"created_at":"2026-05-18T00:03:24.836101+00:00","updated_at":"2026-05-18T00:03:24.836101+00:00"}