{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JAMSQ2XV6O5YLESHTJ4D66YEQN","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":"70a8adeddf8d59d0472968770cdb62df5e7823b3d7c46419a3882379e8484dbe","cross_cats_sorted":["physics.optics","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2018-06-08T06:36:34Z","title_canon_sha256":"ac20384a2d3a91e1674eb3667af1b736e2e29e706fb0ff0f4ba360852dd721d7"},"schema_version":"1.0","source":{"id":"1806.04503","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04503","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04503v3","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04503","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"JAMSQ2XV6O5Y","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JAMSQ2XV6O5YLESH","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JAMSQ2XV","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:2aef2058038539123178f8c27d9ecd6ccab16ff22aded13908f5e8776dd4b17a","target":"graph","created_at":"2026-05-17T23:59:32Z","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":"The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the mathematical foundations of MLE, then reformulate the problem for the measurement of a spatially-varying optical intensity distribution. In this context, the detection of each individual photon is treated as a random event, the outcome being the photon's location. A typical measurement consists of many detected photons, which accumulate to form a spatial intensi","authors_text":"Anthony Vella","cross_cats":["physics.optics","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2018-06-08T06:36:34Z","title":"Tutorial: Maximum likelihood estimation in the context of an optical measurement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04503","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":"sha256:5093f0e1c57064026713bbd195e6d262fec5f4620b0103dcf074d8cdcefd825f","target":"record","created_at":"2026-05-17T23:59:32Z","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":"70a8adeddf8d59d0472968770cdb62df5e7823b3d7c46419a3882379e8484dbe","cross_cats_sorted":["physics.optics","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2018-06-08T06:36:34Z","title_canon_sha256":"ac20384a2d3a91e1674eb3667af1b736e2e29e706fb0ff0f4ba360852dd721d7"},"schema_version":"1.0","source":{"id":"1806.04503","kind":"arxiv","version":3}},"canonical_sha256":"4819286af5f3bb8592479a783f7b04837488f244e5c2d4ee6d89df1529e3f445","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4819286af5f3bb8592479a783f7b04837488f244e5c2d4ee6d89df1529e3f445","first_computed_at":"2026-05-17T23:59:32.559268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:32.559268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FJD4fcjFlv1hirdR3tKagJD0RSKs24wgrSYroiangcViAcbLisNUXTfJb9rKR90dSakdQEsaVkOxKW812zv7Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:32.559847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.04503","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5093f0e1c57064026713bbd195e6d262fec5f4620b0103dcf074d8cdcefd825f","sha256:2aef2058038539123178f8c27d9ecd6ccab16ff22aded13908f5e8776dd4b17a"],"state_sha256":"f21aedf215fcee711d101168f47c17816ac5dd71f67ee859bf255ec3d78f7aad"}