{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:E47ZFCJMSOZSOY62LD2PVYKIPV","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":"0b81102d9255fb3eb1552cbd3885d8e06378a0fcb611a583b0141549b258831c","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-17T16:58:39Z","title_canon_sha256":"aa71df50e627929d22553204f2b9c0269c878c7c94ae2b65eec80a93f6cff7a3"},"schema_version":"1.0","source":{"id":"1111.4148","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4148","created_at":"2026-05-18T04:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4148v1","created_at":"2026-05-18T04:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4148","created_at":"2026-05-18T04:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"E47ZFCJMSOZS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"E47ZFCJMSOZSOY62","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"E47ZFCJM","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:c1b3b306c56b8ecd598bb1fc237a8aeb63d62f0f36d34152ea08fe067be286a8","target":"graph","created_at":"2026-05-18T04:08:05Z","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":"It is shown that a simple Dirichlet process mixture of multivariate normals offers Bayesian density estimation with adaptive posterior convergence rates. Toward this, a novel sieve for non-parametric mixture densities is explored, and its rate adaptability to various smoothness classes of densities in arbitrary dimension is demonstrated. This sieve construction is expected to offer a substantial technical advancement in studying Bayesian non-parametric mixture models based on stick-breaking priors.","authors_text":"Surya T. Tokdar","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-17T16:58:39Z","title":"Adaptive Convergence Rates of a Dirichlet Process Mixture of Multivariate Normals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4148","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":"sha256:6c5a81dc014c28d81bd55453d1a068825c3e1246764b235a0bc1045bb89d2d32","target":"record","created_at":"2026-05-18T04:08:05Z","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":"0b81102d9255fb3eb1552cbd3885d8e06378a0fcb611a583b0141549b258831c","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-11-17T16:58:39Z","title_canon_sha256":"aa71df50e627929d22553204f2b9c0269c878c7c94ae2b65eec80a93f6cff7a3"},"schema_version":"1.0","source":{"id":"1111.4148","kind":"arxiv","version":1}},"canonical_sha256":"273f92892c93b32763da58f4fae1487d7c5c210f1adfd3aef756b151618b49ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"273f92892c93b32763da58f4fae1487d7c5c210f1adfd3aef756b151618b49ad","first_computed_at":"2026-05-18T04:08:05.590448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:05.590448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+znVju/N8Q7MrwzizhsyvpfJzCMWXmLHA6LIMxkwug6H5KemegL/8X49Ax40BEAsWyGFl3A9yJ10pxQgH2AtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:05.590919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4148","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c5a81dc014c28d81bd55453d1a068825c3e1246764b235a0bc1045bb89d2d32","sha256:c1b3b306c56b8ecd598bb1fc237a8aeb63d62f0f36d34152ea08fe067be286a8"],"state_sha256":"795adac8a5b8ac59b71de598a1864681eebc7be66945e0de3247b6de575af650"}