{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KQBZWGA3YNTL3OXJQS4W5JLEYL","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":"3c94d10a0333eb5201ae3b0dfeeede0af49105ecefdca08f939b3e9064613c07","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-03-09T11:18:48Z","title_canon_sha256":"fbce6ddbc363c74ac99a40c350d605097a02342c1f2da173e72d8a94f914560c"},"schema_version":"1.0","source":{"id":"1203.2043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2043","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2043v1","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2043","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"pith_short_12","alias_value":"KQBZWGA3YNTL","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KQBZWGA3YNTL3OXJ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KQBZWGA3","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:b8c5cdb1907f4dda1430f547e997ed92a854c071fe5ba31d01e86bc29c2675c2","target":"graph","created_at":"2026-05-18T04:00:27Z","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":"The frequentist behavior of nonparametric Bayes estimates, more specifically, rates of contraction of the posterior distributions to shrinking $L^r$-norm neighborhoods, $1\\le r\\le\\infty$, of the unknown parameter, are studied. A theorem for nonparametric density estimation is proved under general approximation-theoretic assumptions on the prior. The result is applied to a variety of common examples, including Gaussian process, wavelet series, normal mixture and histogram priors. The rates of contraction are minimax-optimal for $1\\le r\\le2$, but deteriorate as $r$ increases beyond 2. In the cas","authors_text":"Evarist Gin\\'e, Richard Nickl","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-03-09T11:18:48Z","title":"Rates of contraction for posterior distributions in $\\bolds{L^r}$-metrics, $\\bolds{1\\le r\\le\\infty}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2043","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":"sha256:15a544b2ed44b2b05f010b2b0299410987efdb0c4b4a72f63d382b81bbae94d9","target":"record","created_at":"2026-05-18T04:00:27Z","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":"3c94d10a0333eb5201ae3b0dfeeede0af49105ecefdca08f939b3e9064613c07","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-03-09T11:18:48Z","title_canon_sha256":"fbce6ddbc363c74ac99a40c350d605097a02342c1f2da173e72d8a94f914560c"},"schema_version":"1.0","source":{"id":"1203.2043","kind":"arxiv","version":1}},"canonical_sha256":"54039b181bc366bdbae984b96ea564c2c346361db39dc8869647e17782d78277","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54039b181bc366bdbae984b96ea564c2c346361db39dc8869647e17782d78277","first_computed_at":"2026-05-18T04:00:27.630421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:27.630421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cn2pYZLlnvX+DLodXEVST2Q08cjf3OU5SFxckrOU3OGFjGRRKEIL5HMvpgncowCcnk011qNxMmBfiXZ/NyWgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:27.630929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15a544b2ed44b2b05f010b2b0299410987efdb0c4b4a72f63d382b81bbae94d9","sha256:b8c5cdb1907f4dda1430f547e997ed92a854c071fe5ba31d01e86bc29c2675c2"],"state_sha256":"4f664ca2a29386a86061e75f746ffbafd0818adb3a114d1950ad306b64a13d62"}