{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XHWLIWIENJZA3DMW5FWLN7WPSP","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":"2b78f7a90a037fc7a307cf59ada9a47fafbd7255a5406aec5db15a98dd8fa3ba","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-06T17:31:33Z","title_canon_sha256":"6ff50a28b6a5bf50f4a6b103d02a0034f1822de4e62c1c36236921bf89f2f8fb"},"schema_version":"1.0","source":{"id":"1506.02174","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02174","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02174v2","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02174","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"pith_short_12","alias_value":"XHWLIWIENJZA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XHWLIWIENJZA3DMW","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XHWLIWIE","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:92677ac0dd17fc47b111d1458e4994aea79efd78111c2ffcd233039c263ee1fe","target":"graph","created_at":"2026-05-18T00:07:51Z","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":"High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods that can deal with very general high dimensional models. In contrast, Bayes methods have been extensively studied in various nonparametric settings and rate optimal posterior contraction results have been established. This paper provides a unified approach to both Bayes high dimensional statistics and Bayes nonparametrics in a general framework of structured ","authors_text":"Aad W. van der Vaart, Chao Gao, Harrison H. Zhou","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-06T17:31:33Z","title":"A General Framework for Bayes Structured Linear Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02174","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:ea77c7fb393be0c0c2efc5bc92f635407914272c35653c24528380a89b203af2","target":"record","created_at":"2026-05-18T00:07:51Z","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":"2b78f7a90a037fc7a307cf59ada9a47fafbd7255a5406aec5db15a98dd8fa3ba","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-06-06T17:31:33Z","title_canon_sha256":"6ff50a28b6a5bf50f4a6b103d02a0034f1822de4e62c1c36236921bf89f2f8fb"},"schema_version":"1.0","source":{"id":"1506.02174","kind":"arxiv","version":2}},"canonical_sha256":"b9ecb459046a720d8d96e96cb6fecf93ee4fbec4538bc538fe95ff90e41fb743","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9ecb459046a720d8d96e96cb6fecf93ee4fbec4538bc538fe95ff90e41fb743","first_computed_at":"2026-05-18T00:07:51.336010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:51.336010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AKWgN3wQBebPsfNaYl/e4e62FryfHFYfK+Zazb0IQQj2vBnn4xQBPilmRRV3OKpZOWuUE5emkK/VOUzyANBoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:51.336851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02174","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea77c7fb393be0c0c2efc5bc92f635407914272c35653c24528380a89b203af2","sha256:92677ac0dd17fc47b111d1458e4994aea79efd78111c2ffcd233039c263ee1fe"],"state_sha256":"92f0ce366abbcd190fd74c296a6bf1eeb8e6d9545229651b92568281870b01d2"}