{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BXOOQJWXZ3UDFHACWN2H6YMVH4","short_pith_number":"pith:BXOOQJWX","canonical_record":{"source":{"id":"1602.03658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-02-11T10:09:08Z","cross_cats_sorted":[],"title_canon_sha256":"7707ef39795775d633fbe448e3d3693a02600e5c1b8e496ee38e0d18e7224574","abstract_canon_sha256":"238f89f9c29eb9b7b68c99070848a08790d4b52cf14c23cc48e277abbddeff37"},"schema_version":"1.0"},"canonical_sha256":"0ddce826d7cee8329c02b3747f61953f117cbb10a35c4884ee1a8e7499e80de7","source":{"kind":"arxiv","id":"1602.03658","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03658","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03658v1","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03658","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"BXOOQJWXZ3UD","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BXOOQJWXZ3UDFHAC","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BXOOQJWX","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BXOOQJWXZ3UDFHACWN2H6YMVH4","target":"record","payload":{"canonical_record":{"source":{"id":"1602.03658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-02-11T10:09:08Z","cross_cats_sorted":[],"title_canon_sha256":"7707ef39795775d633fbe448e3d3693a02600e5c1b8e496ee38e0d18e7224574","abstract_canon_sha256":"238f89f9c29eb9b7b68c99070848a08790d4b52cf14c23cc48e277abbddeff37"},"schema_version":"1.0"},"canonical_sha256":"0ddce826d7cee8329c02b3747f61953f117cbb10a35c4884ee1a8e7499e80de7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:56.892662Z","signature_b64":"ZaX5SFMBb4HisO/h/Qtu+tkIzyZ4Db5Pu2XAayx/+CWjbcoLDmFZDaCPFc3B/ANu537DVR5y6beCapqEnrqzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ddce826d7cee8329c02b3747f61953f117cbb10a35c4884ee1a8e7499e80de7","last_reissued_at":"2026-05-18T01:20:56.892215Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:56.892215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.03658","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":"2026-05-18T01:20:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QAE6rzpbBJ6zIeGyk9WdJQlGYTDJ2l9NF7qHNuC6YgWGS0HQdZ6y2vXw7YHL8JjHbO+lqQKhyOI4U4qrGk+oDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:09:58.157236Z"},"content_sha256":"2a0882a8d12e3e5226a508376703345e43de2d0bef633b0efccb1b32d96f6df4","schema_version":"1.0","event_id":"sha256:2a0882a8d12e3e5226a508376703345e43de2d0bef633b0efccb1b32d96f6df4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BXOOQJWXZ3UDFHACWN2H6YMVH4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A randomized maximum a posterior method for posterior sampling of high dimensional nonlinear Bayesian inverse problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Kainan Wang, Omar Ghattas, Tan Bui-Thanh","submitted_at":"2016-02-11T10:09:08Z","abstract_excerpt":"We present a randomized maximum a posteriori (rMAP) method for generating approximate samples of posteriors in high dimensional Bayesian inverse problems governed by large-scale forward problems. We derive the rMAP approach by: 1) casting the problem of computing the MAP point as a stochastic optimization problem; 2) interchanging optimization and expectation; and 3) approximating the expectation with a Monte Carlo method. For a specific randomized data and prior mean, rMAP reduces to the maximum likelihood approach (RML). It can also be viewed as an iterative stochastic Newton method. An anal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03658","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":"2026-05-18T01:20:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8pNe8m59sci/4u1AMtQSVTvorDPvMRuDsOc8BWqJyDOvZ5Va3N5Fm4+CaDohRY724QqXowxcwsoxWJGEyBHYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:09:58.157939Z"},"content_sha256":"496beb49ea4bfda1b5ce255d16ae7b65564be52be3e79407a6e28762acb059e0","schema_version":"1.0","event_id":"sha256:496beb49ea4bfda1b5ce255d16ae7b65564be52be3e79407a6e28762acb059e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BXOOQJWXZ3UDFHACWN2H6YMVH4/bundle.json","state_url":"https://pith.science/pith/BXOOQJWXZ3UDFHACWN2H6YMVH4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BXOOQJWXZ3UDFHACWN2H6YMVH4/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":"2026-06-06T20:09:58Z","links":{"resolver":"https://pith.science/pith/BXOOQJWXZ3UDFHACWN2H6YMVH4","bundle":"https://pith.science/pith/BXOOQJWXZ3UDFHACWN2H6YMVH4/bundle.json","state":"https://pith.science/pith/BXOOQJWXZ3UDFHACWN2H6YMVH4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BXOOQJWXZ3UDFHACWN2H6YMVH4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BXOOQJWXZ3UDFHACWN2H6YMVH4","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":"238f89f9c29eb9b7b68c99070848a08790d4b52cf14c23cc48e277abbddeff37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-02-11T10:09:08Z","title_canon_sha256":"7707ef39795775d633fbe448e3d3693a02600e5c1b8e496ee38e0d18e7224574"},"schema_version":"1.0","source":{"id":"1602.03658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03658","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03658v1","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03658","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"BXOOQJWXZ3UD","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BXOOQJWXZ3UDFHAC","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BXOOQJWX","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:496beb49ea4bfda1b5ce255d16ae7b65564be52be3e79407a6e28762acb059e0","target":"graph","created_at":"2026-05-18T01:20:56Z","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":"We present a randomized maximum a posteriori (rMAP) method for generating approximate samples of posteriors in high dimensional Bayesian inverse problems governed by large-scale forward problems. We derive the rMAP approach by: 1) casting the problem of computing the MAP point as a stochastic optimization problem; 2) interchanging optimization and expectation; and 3) approximating the expectation with a Monte Carlo method. For a specific randomized data and prior mean, rMAP reduces to the maximum likelihood approach (RML). It can also be viewed as an iterative stochastic Newton method. An anal","authors_text":"Kainan Wang, Omar Ghattas, Tan Bui-Thanh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-02-11T10:09:08Z","title":"A randomized maximum a posterior method for posterior sampling of high dimensional nonlinear Bayesian inverse problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03658","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":"sha256:2a0882a8d12e3e5226a508376703345e43de2d0bef633b0efccb1b32d96f6df4","target":"record","created_at":"2026-05-18T01:20:56Z","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":"238f89f9c29eb9b7b68c99070848a08790d4b52cf14c23cc48e277abbddeff37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-02-11T10:09:08Z","title_canon_sha256":"7707ef39795775d633fbe448e3d3693a02600e5c1b8e496ee38e0d18e7224574"},"schema_version":"1.0","source":{"id":"1602.03658","kind":"arxiv","version":1}},"canonical_sha256":"0ddce826d7cee8329c02b3747f61953f117cbb10a35c4884ee1a8e7499e80de7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ddce826d7cee8329c02b3747f61953f117cbb10a35c4884ee1a8e7499e80de7","first_computed_at":"2026-05-18T01:20:56.892215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:56.892215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZaX5SFMBb4HisO/h/Qtu+tkIzyZ4Db5Pu2XAayx/+CWjbcoLDmFZDaCPFc3B/ANu537DVR5y6beCapqEnrqzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:56.892662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.03658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a0882a8d12e3e5226a508376703345e43de2d0bef633b0efccb1b32d96f6df4","sha256:496beb49ea4bfda1b5ce255d16ae7b65564be52be3e79407a6e28762acb059e0"],"state_sha256":"7d1e8ae76f9b4ac167ecbd2ceb62dd37cb8c852318e8056c5c6ba56b0ef51692"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HvzYqeNlZiTumPbYNw/3qwit8hFtaOVtxAj3DjVoMCO5hCP1AtToyfwADG0gj9rF1PODcEOlIX84GhWgoD14AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:09:58.162326Z","bundle_sha256":"f188b4649f761abf8a09a887d1e2c94280892d249e9347b405122a6503362e3d"}}