{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5Y5N6VD3Q2F63NPX3FVMBYXXMB","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":"f9de5ef1960b484cb75772612ffb3abc363f9fe72e1dfb8f316073b6fc0dc13d","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-27T22:14:54Z","title_canon_sha256":"62f6c194c09e5c021e5cf8b0d3955072097c2b6a25e381347fda20e56faf689c"},"schema_version":"1.0","source":{"id":"1206.6532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6532","created_at":"2026-05-18T01:56:41Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6532v1","created_at":"2026-05-18T01:56:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6532","created_at":"2026-05-18T01:56:41Z"},{"alias_kind":"pith_short_12","alias_value":"5Y5N6VD3Q2F6","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5Y5N6VD3Q2F63NPX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5Y5N6VD3","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:2fd178af3c48726f0b92d2eb82eafb02bfc68b3b92c043af99635645dc95a2a9","target":"graph","created_at":"2026-05-18T01:56:41Z","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"},"paper":{"abstract_excerpt":"Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is variable projection, where nonlinear least squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood (ML) and maximum a posteriori likelihood (MAP) problems with nuisance parameters, such as variance or degrees of fre","authors_text":"Aleksandr Y. Aravkin, Tristan van Leeuwen","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-27T22:14:54Z","title":"Estimating Nuisance Parameters in Inverse Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6532","kind":"arxiv","version":1},"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:b45d977954968f9516f233f0c0b9dd21de8cdf57a32a031ec74721927fbd2da3","target":"record","created_at":"2026-05-18T01:56:41Z","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":"f9de5ef1960b484cb75772612ffb3abc363f9fe72e1dfb8f316073b6fc0dc13d","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-27T22:14:54Z","title_canon_sha256":"62f6c194c09e5c021e5cf8b0d3955072097c2b6a25e381347fda20e56faf689c"},"schema_version":"1.0","source":{"id":"1206.6532","kind":"arxiv","version":1}},"canonical_sha256":"ee3adf547b868bedb5f7d96ac0e2f7605e7f3d3ba2a7d15515bd7605bb30fd7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee3adf547b868bedb5f7d96ac0e2f7605e7f3d3ba2a7d15515bd7605bb30fd7d","first_computed_at":"2026-05-18T01:56:41.082259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:41.082259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lppZDRyNfXThtUfd66BHgDA1wKexQUT7VMgGB4Dbe+yrX5Tth3XtMnxjt5aYdsqIP2ZRre9AYBwM7XbHdIq7DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:41.082651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b45d977954968f9516f233f0c0b9dd21de8cdf57a32a031ec74721927fbd2da3","sha256:2fd178af3c48726f0b92d2eb82eafb02bfc68b3b92c043af99635645dc95a2a9"],"state_sha256":"a149b9d67f12fc4ab6e970db55298a7d8206b9ff2c0a0ad4c64fb99db64e242a"}