{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CVD4CQDZVEF6HZNMZ4NERPBJ62","short_pith_number":"pith:CVD4CQDZ","canonical_record":{"source":{"id":"1811.01091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-11-02T21:15:01Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"b63f251075361d9c0bda92763a642db3351bb024048662f149c01ee379328e35","abstract_canon_sha256":"621684001d75948885b6bdec3055ac326b503183a55cbe0876186db9018590c5"},"schema_version":"1.0"},"canonical_sha256":"1547c14079a90be3e5accf1a48bc29f6a992a4de19be2e5ea3b762f753ac930b","source":{"kind":"arxiv","id":"1811.01091","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01091","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01091v2","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01091","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"CVD4CQDZVEF6","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CVD4CQDZVEF6HZNM","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CVD4CQDZ","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CVD4CQDZVEF6HZNMZ4NERPBJ62","target":"record","payload":{"canonical_record":{"source":{"id":"1811.01091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-11-02T21:15:01Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"b63f251075361d9c0bda92763a642db3351bb024048662f149c01ee379328e35","abstract_canon_sha256":"621684001d75948885b6bdec3055ac326b503183a55cbe0876186db9018590c5"},"schema_version":"1.0"},"canonical_sha256":"1547c14079a90be3e5accf1a48bc29f6a992a4de19be2e5ea3b762f753ac930b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:00.134214Z","signature_b64":"ojCL2OuYAVpTEItSmtyCL2Ql3M31IOJXY7ZGfmooywmj6PKNy39lykG8ZSIFYY7O/2+6z+U9VC/qFMISpx3sAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1547c14079a90be3e5accf1a48bc29f6a992a4de19be2e5ea3b762f753ac930b","last_reissued_at":"2026-05-17T23:44:00.133519Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:00.133519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.01091","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/yv2VcTEopZ3M6+FLsTugVxzxkozn+nYw6uAHRh+KM4t7FATVqCIu+QuqOpnc16gHcDoHFqwaTze5itw20hCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:37:15.002360Z"},"content_sha256":"f814bcf4725e89c2eb5f83df24d22e704096932dc8fb35163ae88f0163231edb","schema_version":"1.0","event_id":"sha256:f814bcf4725e89c2eb5f83df24d22e704096932dc8fb35163ae88f0163231edb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CVD4CQDZVEF6HZNMZ4NERPBJ62","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Marginalization-based MCMC Methods for Hierarchical Bayesian Inverse Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"stat.CO","authors_text":"Alen Alexanderian, Arvind K. Saibaba, D. Andrew Brown, Johnathan Bardsley","submitted_at":"2018-11-02T21:15:01Z","abstract_excerpt":"Hierarchical models in Bayesian inverse problems are characterized by an assumed prior probability distribution for the unknown state and measurement error precision, and hyper-priors for the prior parameters. Combining these probability models using Bayes' law often yields a posterior distribution that cannot be sampled from directly, even for a linear model with Gaussian measurement error and Gaussian prior. Gibbs sampling can be used to sample from the posterior, but problems arise when the dimension of the state is large. This is because the Gaussian sample required for each iteration can "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01091","kind":"arxiv","version":2},"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":"2026-05-17T23:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06dj7ra4L9iE1q7zsEVOHkphy4zzags2L9eBDAunXREfpX2d9HoraNd2nnV3uOrnK9jHGLZc7bT8nk+N4D+VDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:37:15.002713Z"},"content_sha256":"2069df9e473625c95ac35e2c85ffc23308eec9171f5deefa9d8a8bb5cfcc3a2c","schema_version":"1.0","event_id":"sha256:2069df9e473625c95ac35e2c85ffc23308eec9171f5deefa9d8a8bb5cfcc3a2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CVD4CQDZVEF6HZNMZ4NERPBJ62/bundle.json","state_url":"https://pith.science/pith/CVD4CQDZVEF6HZNMZ4NERPBJ62/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CVD4CQDZVEF6HZNMZ4NERPBJ62/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":"2026-06-01T17:37:15Z","links":{"resolver":"https://pith.science/pith/CVD4CQDZVEF6HZNMZ4NERPBJ62","bundle":"https://pith.science/pith/CVD4CQDZVEF6HZNMZ4NERPBJ62/bundle.json","state":"https://pith.science/pith/CVD4CQDZVEF6HZNMZ4NERPBJ62/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CVD4CQDZVEF6HZNMZ4NERPBJ62/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CVD4CQDZVEF6HZNMZ4NERPBJ62","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":"621684001d75948885b6bdec3055ac326b503183a55cbe0876186db9018590c5","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-11-02T21:15:01Z","title_canon_sha256":"b63f251075361d9c0bda92763a642db3351bb024048662f149c01ee379328e35"},"schema_version":"1.0","source":{"id":"1811.01091","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01091","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01091v2","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01091","created_at":"2026-05-17T23:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"CVD4CQDZVEF6","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CVD4CQDZVEF6HZNM","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CVD4CQDZ","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:2069df9e473625c95ac35e2c85ffc23308eec9171f5deefa9d8a8bb5cfcc3a2c","target":"graph","created_at":"2026-05-17T23:44:00Z","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":"Hierarchical models in Bayesian inverse problems are characterized by an assumed prior probability distribution for the unknown state and measurement error precision, and hyper-priors for the prior parameters. Combining these probability models using Bayes' law often yields a posterior distribution that cannot be sampled from directly, even for a linear model with Gaussian measurement error and Gaussian prior. Gibbs sampling can be used to sample from the posterior, but problems arise when the dimension of the state is large. This is because the Gaussian sample required for each iteration can ","authors_text":"Alen Alexanderian, Arvind K. Saibaba, D. Andrew Brown, Johnathan Bardsley","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-11-02T21:15:01Z","title":"Efficient Marginalization-based MCMC Methods for Hierarchical Bayesian Inverse Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01091","kind":"arxiv","version":2},"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:f814bcf4725e89c2eb5f83df24d22e704096932dc8fb35163ae88f0163231edb","target":"record","created_at":"2026-05-17T23:44:00Z","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":"621684001d75948885b6bdec3055ac326b503183a55cbe0876186db9018590c5","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-11-02T21:15:01Z","title_canon_sha256":"b63f251075361d9c0bda92763a642db3351bb024048662f149c01ee379328e35"},"schema_version":"1.0","source":{"id":"1811.01091","kind":"arxiv","version":2}},"canonical_sha256":"1547c14079a90be3e5accf1a48bc29f6a992a4de19be2e5ea3b762f753ac930b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1547c14079a90be3e5accf1a48bc29f6a992a4de19be2e5ea3b762f753ac930b","first_computed_at":"2026-05-17T23:44:00.133519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:00.133519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ojCL2OuYAVpTEItSmtyCL2Ql3M31IOJXY7ZGfmooywmj6PKNy39lykG8ZSIFYY7O/2+6z+U9VC/qFMISpx3sAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:00.134214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01091","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f814bcf4725e89c2eb5f83df24d22e704096932dc8fb35163ae88f0163231edb","sha256:2069df9e473625c95ac35e2c85ffc23308eec9171f5deefa9d8a8bb5cfcc3a2c"],"state_sha256":"df554297e17d679ed1f5a1459cab7bc983283b7b3e2e779960865fa432940900"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"71uu1snFsrButmgsoaOX7+clJsBF5f9kcrju4iToU3Dy/j5Cf1dHi7IXrjXivVx5ZeteMNBDukaqGPGlPwi9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:37:15.004736Z","bundle_sha256":"c3a0d136a18094ed81d6458a538faed4c28253da59677795ec421cb079192636"}}