{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6GYW33AZBBBLDQV5MT75S3JLWP","short_pith_number":"pith:6GYW33AZ","canonical_record":{"source":{"id":"1206.3985","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-06-18T16:49:47Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"adcd8e396fb125caa7114e25cdabe7f46beada9dcbe6fe2577db3d5c7a49eb88","abstract_canon_sha256":"b329941c9f2726e30f0d19865176fbe93a157c862f5a46e6e3d4c75098996326"},"schema_version":"1.0"},"canonical_sha256":"f1b16dec190842b1c2bd64ffd96d2bb3f3108b0b23dc3fac6e300cb9be7e2eb1","source":{"kind":"arxiv","id":"1206.3985","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3985","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3985v3","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3985","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"6GYW33AZBBBL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6GYW33AZBBBLDQV5","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6GYW33AZ","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6GYW33AZBBBLDQV5MT75S3JLWP","target":"record","payload":{"canonical_record":{"source":{"id":"1206.3985","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-06-18T16:49:47Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"adcd8e396fb125caa7114e25cdabe7f46beada9dcbe6fe2577db3d5c7a49eb88","abstract_canon_sha256":"b329941c9f2726e30f0d19865176fbe93a157c862f5a46e6e3d4c75098996326"},"schema_version":"1.0"},"canonical_sha256":"f1b16dec190842b1c2bd64ffd96d2bb3f3108b0b23dc3fac6e300cb9be7e2eb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:10.900696Z","signature_b64":"kvPws6UFnb+ueM6M/VozzD6Ganlj26AnfsHC9usCu0SJ0UlBXFtngxP0fcpUJUVue3xmklit9vj88qfO1W7zAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1b16dec190842b1c2bd64ffd96d2bb3f3108b0b23dc3fac6e300cb9be7e2eb1","last_reissued_at":"2026-05-18T03:13:10.899969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:10.899969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.3985","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eKlMmtL0LSXrEWRNzFRY6tirQ2Mxq3lYzC+m2u0N+J+pOrUi9tF79kr1FP2UqJqfgLiE7zGa/RX/bi/zsB/iCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:36:30.662971Z"},"content_sha256":"801eced0c698ccc9e728872fbab35aebe11f5f65e9a65cb895e9c6773a4c98c9","schema_version":"1.0","event_id":"sha256:801eced0c698ccc9e728872fbab35aebe11f5f65e9a65cb895e9c6773a4c98c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6GYW33AZBBBLDQV5MT75S3JLWP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing the Cramer-Rao bound of Markov random field parameters: Application to the Ising and the Potts models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"stat.CO","authors_text":"Hadj Batatia, Jean-Yves Tourneret, Marcelo Pereyra, Nicolas Dobigeon","submitted_at":"2012-06-18T16:49:47Z","abstract_excerpt":"This report considers the problem of computing the Cramer-Rao bound for the parameters of a Markov random field. Computation of the exact bound is not feasible for most fields of interest because their likelihoods are intractable and have intractable derivatives. We show here how it is possible to formulate the computation of the bound as a statistical inference problem that can be solve approximately, but with arbitrarily high accuracy, by using a Monte Carlo method. The proposed methodology is successfully applied on the Ising and the Potts models.% where it is used to assess the performance"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3985","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k9qb+dIcQAbHzWBRihXOd9SIgGQQ/qpkj/EPjDVE0Aih8IOvLlyAjqBClDpRzXVTBED0gx44WvutZPa30eLHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:36:30.663651Z"},"content_sha256":"7301a1defb93bf90d9061319db3f4ccd74b5018e8e6fd811283a1045c101f8c4","schema_version":"1.0","event_id":"sha256:7301a1defb93bf90d9061319db3f4ccd74b5018e8e6fd811283a1045c101f8c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GYW33AZBBBLDQV5MT75S3JLWP/bundle.json","state_url":"https://pith.science/pith/6GYW33AZBBBLDQV5MT75S3JLWP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GYW33AZBBBLDQV5MT75S3JLWP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T19:36:30Z","links":{"resolver":"https://pith.science/pith/6GYW33AZBBBLDQV5MT75S3JLWP","bundle":"https://pith.science/pith/6GYW33AZBBBLDQV5MT75S3JLWP/bundle.json","state":"https://pith.science/pith/6GYW33AZBBBLDQV5MT75S3JLWP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GYW33AZBBBLDQV5MT75S3JLWP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6GYW33AZBBBLDQV5MT75S3JLWP","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":"b329941c9f2726e30f0d19865176fbe93a157c862f5a46e6e3d4c75098996326","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-06-18T16:49:47Z","title_canon_sha256":"adcd8e396fb125caa7114e25cdabe7f46beada9dcbe6fe2577db3d5c7a49eb88"},"schema_version":"1.0","source":{"id":"1206.3985","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3985","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3985v3","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3985","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"6GYW33AZBBBL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6GYW33AZBBBLDQV5","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6GYW33AZ","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:7301a1defb93bf90d9061319db3f4ccd74b5018e8e6fd811283a1045c101f8c4","target":"graph","created_at":"2026-05-18T03:13:10Z","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":"This report considers the problem of computing the Cramer-Rao bound for the parameters of a Markov random field. Computation of the exact bound is not feasible for most fields of interest because their likelihoods are intractable and have intractable derivatives. We show here how it is possible to formulate the computation of the bound as a statistical inference problem that can be solve approximately, but with arbitrarily high accuracy, by using a Monte Carlo method. The proposed methodology is successfully applied on the Ising and the Potts models.% where it is used to assess the performance","authors_text":"Hadj Batatia, Jean-Yves Tourneret, Marcelo Pereyra, Nicolas Dobigeon","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-06-18T16:49:47Z","title":"Computing the Cramer-Rao bound of Markov random field parameters: Application to the Ising and the Potts models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3985","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":"sha256:801eced0c698ccc9e728872fbab35aebe11f5f65e9a65cb895e9c6773a4c98c9","target":"record","created_at":"2026-05-18T03:13:10Z","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":"b329941c9f2726e30f0d19865176fbe93a157c862f5a46e6e3d4c75098996326","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-06-18T16:49:47Z","title_canon_sha256":"adcd8e396fb125caa7114e25cdabe7f46beada9dcbe6fe2577db3d5c7a49eb88"},"schema_version":"1.0","source":{"id":"1206.3985","kind":"arxiv","version":3}},"canonical_sha256":"f1b16dec190842b1c2bd64ffd96d2bb3f3108b0b23dc3fac6e300cb9be7e2eb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1b16dec190842b1c2bd64ffd96d2bb3f3108b0b23dc3fac6e300cb9be7e2eb1","first_computed_at":"2026-05-18T03:13:10.899969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:10.899969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kvPws6UFnb+ueM6M/VozzD6Ganlj26AnfsHC9usCu0SJ0UlBXFtngxP0fcpUJUVue3xmklit9vj88qfO1W7zAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:10.900696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3985","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:801eced0c698ccc9e728872fbab35aebe11f5f65e9a65cb895e9c6773a4c98c9","sha256:7301a1defb93bf90d9061319db3f4ccd74b5018e8e6fd811283a1045c101f8c4"],"state_sha256":"5387912e6e655de6c26525f8ee7f807f34d123a239e16f6a81a2e24f54c4dda1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WOVMU0FeKxC6GkN6qC8mVorGVbdZRCFqZwyTybrUvGTNvfVXF5QKoqxd5FSFM+fk6EES5ZS7MHgbPSjJ9GhoBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:36:30.667429Z","bundle_sha256":"01db5c60ac4ad02601871d8040348dd99d96c295721a85eafa443bbad0ed587a"}}