{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6H4P3W4M576BMA25ER2B7TLLBH","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":"2647cbf86afc4b02843369cfd6eb1facbc55515ae40d557867f28441e4cc7d4c","cross_cats_sorted":["math.NA","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-19T11:44:51Z","title_canon_sha256":"46e937877c041415666c9f5dd74c2ae7e74b77fb04700acdfde03ca48969f764"},"schema_version":"1.0","source":{"id":"1605.05898","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05898","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05898v5","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05898","created_at":"2026-05-18T00:15:31Z"},{"alias_kind":"pith_short_12","alias_value":"6H4P3W4M576B","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6H4P3W4M576BMA25","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6H4P3W4M","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:f1fe4e474cf3f1c25ff02e9cd9febf81c933928a3bb260514895b93c42b5ba5e","target":"graph","created_at":"2026-05-18T00:15:31Z","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 article extends the framework of Bayesian inverse problems in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451--559, 2010) and others, to the case of a heavy-tailed prior measure in the family of stable distributions, such as an infinite-dimensional Cauchy distribution, for which polynomial moments are infinite or undefined. It is shown that analogues of the Karhunen--Lo\\`eve expansion for square-integrable random variables can be used to sample such measures on quasi-Banach spaces. Furthermore, under weaker regularity assumptions than those used to date, ","authors_text":"T. J. Sullivan","cross_cats":["math.NA","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-19T11:44:51Z","title":"Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05898","kind":"arxiv","version":5},"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:a450354e1031ec2748ef6d2f5e532b0944eaaf285c8e3eaa04ae8ca2f4b4b393","target":"record","created_at":"2026-05-18T00:15:31Z","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":"2647cbf86afc4b02843369cfd6eb1facbc55515ae40d557867f28441e4cc7d4c","cross_cats_sorted":["math.NA","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-19T11:44:51Z","title_canon_sha256":"46e937877c041415666c9f5dd74c2ae7e74b77fb04700acdfde03ca48969f764"},"schema_version":"1.0","source":{"id":"1605.05898","kind":"arxiv","version":5}},"canonical_sha256":"f1f8fddb8ceffc16035d24741fcd6b09e2557c73299f02b7f26f9b3f00339394","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1f8fddb8ceffc16035d24741fcd6b09e2557c73299f02b7f26f9b3f00339394","first_computed_at":"2026-05-18T00:15:31.143413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:31.143413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XBOiz2Dd78UKdnKLlIe6ucAVaETcwCUCrOVtHUf6AEXcriOmOG3vd8y0qRM0sQEt2HtrYh+DDMNOq1h4NUhmCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:31.143923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05898","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a450354e1031ec2748ef6d2f5e532b0944eaaf285c8e3eaa04ae8ca2f4b4b393","sha256:f1fe4e474cf3f1c25ff02e9cd9febf81c933928a3bb260514895b93c42b5ba5e"],"state_sha256":"bed23e5bb014b8e145bc9460745951f5c044a4dcc08d9079ee41527f96e2113a"}