{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FFFMEKHMXRAWYHIYR7MRKCCJF5","short_pith_number":"pith:FFFMEKHM","schema_version":"1.0","canonical_sha256":"294ac228ecbc416c1d188fd91508492f4a41f1e190085595f343248d8727e4fd","source":{"kind":"arxiv","id":"1705.07646","version":2},"attestation_state":"computed","paper":{"title":"An approximate empirical Bayesian method for large-scale linear-Gaussian inverse problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"math.NA","authors_text":"Jinglai Li, Qingping Zhou, Wenqing Liu, Youssef M. Marzouk","submitted_at":"2017-05-22T10:23:00Z","abstract_excerpt":"We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often determined via an empirical Bayesian method that maximizes the marginal likelihood function, i.e., the probability density of the data conditional on the hyperparameters. Evaluating the marginal likelihood, however, is computationally challenging for large-scale problems. In this work, we present a method to approximately evaluate marginal likelihood functions"},"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":"1705.07646","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-05-22T10:23:00Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"87ca016e98ae8a6563075afe92b1c9ceeb9200c4033be496ffc9ec16de663bd9","abstract_canon_sha256":"73141ff2c1edc4b049641d334ecbbb2eaceff6a77bb8c088e693257a93bc9f80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:31.229679Z","signature_b64":"DEnWWn3bqvwDzpjpK7qdC4Z3mt+WTTso8hOgB4/Hm6XJXQ3rCH+MgR/eiejj2i7bnGNdjYOikXS5UyCdLBdBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"294ac228ecbc416c1d188fd91508492f4a41f1e190085595f343248d8727e4fd","last_reissued_at":"2026-05-18T00:09:31.228952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:31.228952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An approximate empirical Bayesian method for large-scale linear-Gaussian inverse problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"math.NA","authors_text":"Jinglai Li, Qingping Zhou, Wenqing Liu, Youssef M. Marzouk","submitted_at":"2017-05-22T10:23:00Z","abstract_excerpt":"We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often determined via an empirical Bayesian method that maximizes the marginal likelihood function, i.e., the probability density of the data conditional on the hyperparameters. Evaluating the marginal likelihood, however, is computationally challenging for large-scale problems. In this work, we present a method to approximately evaluate marginal likelihood functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07646","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.07646","created_at":"2026-05-18T00:09:31.229080+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.07646v2","created_at":"2026-05-18T00:09:31.229080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07646","created_at":"2026-05-18T00:09:31.229080+00:00"},{"alias_kind":"pith_short_12","alias_value":"FFFMEKHMXRAW","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FFFMEKHMXRAWYHIY","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FFFMEKHM","created_at":"2026-05-18T12:31:15.632608+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/FFFMEKHMXRAWYHIYR7MRKCCJF5","json":"https://pith.science/pith/FFFMEKHMXRAWYHIYR7MRKCCJF5.json","graph_json":"https://pith.science/api/pith-number/FFFMEKHMXRAWYHIYR7MRKCCJF5/graph.json","events_json":"https://pith.science/api/pith-number/FFFMEKHMXRAWYHIYR7MRKCCJF5/events.json","paper":"https://pith.science/paper/FFFMEKHM"},"agent_actions":{"view_html":"https://pith.science/pith/FFFMEKHMXRAWYHIYR7MRKCCJF5","download_json":"https://pith.science/pith/FFFMEKHMXRAWYHIYR7MRKCCJF5.json","view_paper":"https://pith.science/paper/FFFMEKHM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.07646&json=true","fetch_graph":"https://pith.science/api/pith-number/FFFMEKHMXRAWYHIYR7MRKCCJF5/graph.json","fetch_events":"https://pith.science/api/pith-number/FFFMEKHMXRAWYHIYR7MRKCCJF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FFFMEKHMXRAWYHIYR7MRKCCJF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FFFMEKHMXRAWYHIYR7MRKCCJF5/action/storage_attestation","attest_author":"https://pith.science/pith/FFFMEKHMXRAWYHIYR7MRKCCJF5/action/author_attestation","sign_citation":"https://pith.science/pith/FFFMEKHMXRAWYHIYR7MRKCCJF5/action/citation_signature","submit_replication":"https://pith.science/pith/FFFMEKHMXRAWYHIYR7MRKCCJF5/action/replication_record"}},"created_at":"2026-05-18T00:09:31.229080+00:00","updated_at":"2026-05-18T00:09:31.229080+00:00"}