{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:E2Z7AY4N2K5RU7QGYGLKBG347J","short_pith_number":"pith:E2Z7AY4N","schema_version":"1.0","canonical_sha256":"26b3f0638dd2bb1a7e06c196a09b7cfa52a761362e9c8e2a94d8225e8cc140e3","source":{"kind":"arxiv","id":"2401.03074","version":1},"attestation_state":"computed","paper":{"title":"Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA","stat.TH"],"primary_cat":"math.ST","authors_text":"Daniel Sanz-Alonso, Nathan Waniorek","submitted_at":"2024-01-05T22:13:41Z","abstract_excerpt":"This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings."},"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":"2401.03074","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-01-05T22:13:41Z","cross_cats_sorted":["cs.NA","math.NA","stat.TH"],"title_canon_sha256":"a048b6118c247a28d661c22004896437361f4d12e3e6c5e56c107a0f49b73e53","abstract_canon_sha256":"90352b2c83921ba052fc1cc1714dcb4759bdf780a92560a95f8d853e12af3a5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:31:02.034857Z","signature_b64":"3cB+UdjtqwkyYkWXRkPe7xaU0RvT3E8W1nf3jmCKpRVYnM4OABMhMmt976tUTbWUFetyWHK6ohyEYNKppZ3VCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26b3f0638dd2bb1a7e06c196a09b7cfa52a761362e9c8e2a94d8225e8cc140e3","last_reissued_at":"2026-07-05T07:31:02.034509Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:31:02.034509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA","stat.TH"],"primary_cat":"math.ST","authors_text":"Daniel Sanz-Alonso, Nathan Waniorek","submitted_at":"2024-01-05T22:13:41Z","abstract_excerpt":"This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.03074","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.03074/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2401.03074","created_at":"2026-07-05T07:31:02.034568+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.03074v1","created_at":"2026-07-05T07:31:02.034568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.03074","created_at":"2026-07-05T07:31:02.034568+00:00"},{"alias_kind":"pith_short_12","alias_value":"E2Z7AY4N2K5R","created_at":"2026-07-05T07:31:02.034568+00:00"},{"alias_kind":"pith_short_16","alias_value":"E2Z7AY4N2K5RU7QG","created_at":"2026-07-05T07:31:02.034568+00:00"},{"alias_kind":"pith_short_8","alias_value":"E2Z7AY4N","created_at":"2026-07-05T07:31:02.034568+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/E2Z7AY4N2K5RU7QGYGLKBG347J","json":"https://pith.science/pith/E2Z7AY4N2K5RU7QGYGLKBG347J.json","graph_json":"https://pith.science/api/pith-number/E2Z7AY4N2K5RU7QGYGLKBG347J/graph.json","events_json":"https://pith.science/api/pith-number/E2Z7AY4N2K5RU7QGYGLKBG347J/events.json","paper":"https://pith.science/paper/E2Z7AY4N"},"agent_actions":{"view_html":"https://pith.science/pith/E2Z7AY4N2K5RU7QGYGLKBG347J","download_json":"https://pith.science/pith/E2Z7AY4N2K5RU7QGYGLKBG347J.json","view_paper":"https://pith.science/paper/E2Z7AY4N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.03074&json=true","fetch_graph":"https://pith.science/api/pith-number/E2Z7AY4N2K5RU7QGYGLKBG347J/graph.json","fetch_events":"https://pith.science/api/pith-number/E2Z7AY4N2K5RU7QGYGLKBG347J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E2Z7AY4N2K5RU7QGYGLKBG347J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E2Z7AY4N2K5RU7QGYGLKBG347J/action/storage_attestation","attest_author":"https://pith.science/pith/E2Z7AY4N2K5RU7QGYGLKBG347J/action/author_attestation","sign_citation":"https://pith.science/pith/E2Z7AY4N2K5RU7QGYGLKBG347J/action/citation_signature","submit_replication":"https://pith.science/pith/E2Z7AY4N2K5RU7QGYGLKBG347J/action/replication_record"}},"created_at":"2026-07-05T07:31:02.034568+00:00","updated_at":"2026-07-05T07:31:02.034568+00:00"}