{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2XRRXUNSHLK6JNTZRIIW6X23VZ","short_pith_number":"pith:2XRRXUNS","canonical_record":{"source":{"id":"1012.0753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-12-03T14:43:07Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"77e17d7abe2fb6f43b54e51f0754a4bb19efb51fd7226529a5d0c44329bc6471","abstract_canon_sha256":"b1ec7721744c4c474d2a1c852686df982b8e38e21e7ca5e95af361b5c731f164"},"schema_version":"1.0"},"canonical_sha256":"d5e31bd1b23ad5e4b6798a116f5f5bae7834ae1305d79b24657789a38f72745f","source":{"kind":"arxiv","id":"1012.0753","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0753","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0753v1","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0753","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"2XRRXUNSHLK6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2XRRXUNSHLK6JNTZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2XRRXUNS","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2XRRXUNSHLK6JNTZRIIW6X23VZ","target":"record","payload":{"canonical_record":{"source":{"id":"1012.0753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-12-03T14:43:07Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"77e17d7abe2fb6f43b54e51f0754a4bb19efb51fd7226529a5d0c44329bc6471","abstract_canon_sha256":"b1ec7721744c4c474d2a1c852686df982b8e38e21e7ca5e95af361b5c731f164"},"schema_version":"1.0"},"canonical_sha256":"d5e31bd1b23ad5e4b6798a116f5f5bae7834ae1305d79b24657789a38f72745f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:16.208938Z","signature_b64":"Gl5SRPn1YGyRzXOCkEeKcxhxV+QhvZut29rSaWB82BEfkqtzhAsnKpbumvmt3OMatTnUuvkBBZPmv3lD3YO2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5e31bd1b23ad5e4b6798a116f5f5bae7834ae1305d79b24657789a38f72745f","last_reissued_at":"2026-05-18T02:23:16.208445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:16.208445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.0753","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CIB9yRF/wRqA1zZV/X16qlqmu+Tz8h+N77SwY2auSlUIfdTMc/Bqkc+/4My+FMDGLbXXI+NqWAl6rkuphyowDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:44:07.148871Z"},"content_sha256":"7167d01907dcc97476670dc80e79b08db06baceb9752ef9e8b4732cae9222852","schema_version":"1.0","event_id":"sha256:7167d01907dcc97476670dc80e79b08db06baceb9752ef9e8b4732cae9222852"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2XRRXUNSHLK6JNTZRIIW6X23VZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An asymptotic approximation of the marginal likelihood for general Markov models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Piotr Zwiernik","submitted_at":"2010-12-03T14:43:07Z","abstract_excerpt":"The standard Bayesian Information Criterion (BIC) is derived under regularity conditions which are not always satisfied by the graphical models with hidden variables. In this paper we derive the BIC score for Bayesian networks in the case of binary data and when the underlying graph is a rooted tree and all the inner nodes represent hidden variables. This provides a direct generalization of a similar formula given by Rusakov and Geiger for naive Bayes models. The main tool used in this paper is a connection between asymptotic approximation of Laplace integrals and the real log-canonical thresh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0753","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":""},"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":"2026-05-18T02:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tb48BVg93fGYB/8CuQq7GLfBjOZQyz3HqNLTmzZhAZot1ZgN3VWe7vhL0LTweBHEBEJI68oUr0W8paiZNEs6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:44:07.149481Z"},"content_sha256":"7d568b9e34f710de3c7123f212a226b28c901010022ce0f77ea4f941cf08c5ec","schema_version":"1.0","event_id":"sha256:7d568b9e34f710de3c7123f212a226b28c901010022ce0f77ea4f941cf08c5ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2XRRXUNSHLK6JNTZRIIW6X23VZ/bundle.json","state_url":"https://pith.science/pith/2XRRXUNSHLK6JNTZRIIW6X23VZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2XRRXUNSHLK6JNTZRIIW6X23VZ/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":"2026-05-25T21:44:07Z","links":{"resolver":"https://pith.science/pith/2XRRXUNSHLK6JNTZRIIW6X23VZ","bundle":"https://pith.science/pith/2XRRXUNSHLK6JNTZRIIW6X23VZ/bundle.json","state":"https://pith.science/pith/2XRRXUNSHLK6JNTZRIIW6X23VZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2XRRXUNSHLK6JNTZRIIW6X23VZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2XRRXUNSHLK6JNTZRIIW6X23VZ","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":"b1ec7721744c4c474d2a1c852686df982b8e38e21e7ca5e95af361b5c731f164","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-12-03T14:43:07Z","title_canon_sha256":"77e17d7abe2fb6f43b54e51f0754a4bb19efb51fd7226529a5d0c44329bc6471"},"schema_version":"1.0","source":{"id":"1012.0753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0753","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0753v1","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0753","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"2XRRXUNSHLK6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2XRRXUNSHLK6JNTZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2XRRXUNS","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:7d568b9e34f710de3c7123f212a226b28c901010022ce0f77ea4f941cf08c5ec","target":"graph","created_at":"2026-05-18T02:23:16Z","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 standard Bayesian Information Criterion (BIC) is derived under regularity conditions which are not always satisfied by the graphical models with hidden variables. In this paper we derive the BIC score for Bayesian networks in the case of binary data and when the underlying graph is a rooted tree and all the inner nodes represent hidden variables. This provides a direct generalization of a similar formula given by Rusakov and Geiger for naive Bayes models. The main tool used in this paper is a connection between asymptotic approximation of Laplace integrals and the real log-canonical thresh","authors_text":"Piotr Zwiernik","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-12-03T14:43:07Z","title":"An asymptotic approximation of the marginal likelihood for general Markov models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0753","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":"sha256:7167d01907dcc97476670dc80e79b08db06baceb9752ef9e8b4732cae9222852","target":"record","created_at":"2026-05-18T02:23:16Z","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":"b1ec7721744c4c474d2a1c852686df982b8e38e21e7ca5e95af361b5c731f164","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-12-03T14:43:07Z","title_canon_sha256":"77e17d7abe2fb6f43b54e51f0754a4bb19efb51fd7226529a5d0c44329bc6471"},"schema_version":"1.0","source":{"id":"1012.0753","kind":"arxiv","version":1}},"canonical_sha256":"d5e31bd1b23ad5e4b6798a116f5f5bae7834ae1305d79b24657789a38f72745f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5e31bd1b23ad5e4b6798a116f5f5bae7834ae1305d79b24657789a38f72745f","first_computed_at":"2026-05-18T02:23:16.208445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:16.208445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gl5SRPn1YGyRzXOCkEeKcxhxV+QhvZut29rSaWB82BEfkqtzhAsnKpbumvmt3OMatTnUuvkBBZPmv3lD3YO2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:16.208938Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7167d01907dcc97476670dc80e79b08db06baceb9752ef9e8b4732cae9222852","sha256:7d568b9e34f710de3c7123f212a226b28c901010022ce0f77ea4f941cf08c5ec"],"state_sha256":"bf0490af6ddecedfadb04431eb218e1fff05d8d2b83989fb8a081a535fea9163"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v9d6NT+l1Fk27EHU8Qxm7OiAtzzPqXovaa+WDjNVJPEFfeSPd8cpt9N1q9YXOMCBeRUW5KAd/GZdanLHs1CtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:44:07.153072Z","bundle_sha256":"f67b0e08b8b457d2dee198a1500f198465f93985d507fea803fc8cf1320becdc"}}