{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZSUZ6CBUMICIT42RMRFJIXUKQ7","short_pith_number":"pith:ZSUZ6CBU","schema_version":"1.0","canonical_sha256":"cca99f0834620489f351644a945e8a87d0e9ebacf7d4664f0b9d0729a6588620","source":{"kind":"arxiv","id":"1301.1898","version":3},"attestation_state":"computed","paper":{"title":"Concentration rate and consistency of the posterior under monotonicity constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jean-Bernard Salomond","submitted_at":"2013-01-09T15:55:12Z","abstract_excerpt":"In this paper, we consider the well known problem of estimating a density function under qualitative assumptions. More precisely, we estimate monotone non increasing densities in a Bayesian setting and derive concentration rate for the posterior distribution for a Dirichlet process and finite mixture prior. We prove that the posterior distribution based on both priors concentrates at the rate $(n/\\log(n))^{-1/3}$, which is the minimax rate of estimation up to a \\log(n)$ factor. We also study the behaviour of the posterior for the point-wise loss at any fixed point of the support the density an"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.1898","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-01-09T15:55:12Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"17f3a41027b4c18fe7e0f28e1b30e8c34447b82dd0e3c74bfafa1d86ed2ad436","abstract_canon_sha256":"c886b4a9382f7a2b68fcbad0fe8d56f6cc7b62f770ecdba3ffeebbe097df5b60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:51.754388Z","signature_b64":"ZcuWqc56LnoxQDpAgw3Qxd0ra9l7VnV2buQs5CE0ZR0a5jQgInJoa2neFkFHqI4fEbb8DtLLxLiBcScW46n6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cca99f0834620489f351644a945e8a87d0e9ebacf7d4664f0b9d0729a6588620","last_reissued_at":"2026-05-18T02:26:51.753967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:51.753967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentration rate and consistency of the posterior under monotonicity constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jean-Bernard Salomond","submitted_at":"2013-01-09T15:55:12Z","abstract_excerpt":"In this paper, we consider the well known problem of estimating a density function under qualitative assumptions. More precisely, we estimate monotone non increasing densities in a Bayesian setting and derive concentration rate for the posterior distribution for a Dirichlet process and finite mixture prior. We prove that the posterior distribution based on both priors concentrates at the rate $(n/\\log(n))^{-1/3}$, which is the minimax rate of estimation up to a \\log(n)$ factor. We also study the behaviour of the posterior for the point-wise loss at any fixed point of the support the density an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1898","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.1898","created_at":"2026-05-18T02:26:51.754031+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.1898v3","created_at":"2026-05-18T02:26:51.754031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1898","created_at":"2026-05-18T02:26:51.754031+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZSUZ6CBUMICI","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZSUZ6CBUMICIT42R","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZSUZ6CBU","created_at":"2026-05-18T12:28:09.283467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZSUZ6CBUMICIT42RMRFJIXUKQ7","json":"https://pith.science/pith/ZSUZ6CBUMICIT42RMRFJIXUKQ7.json","graph_json":"https://pith.science/api/pith-number/ZSUZ6CBUMICIT42RMRFJIXUKQ7/graph.json","events_json":"https://pith.science/api/pith-number/ZSUZ6CBUMICIT42RMRFJIXUKQ7/events.json","paper":"https://pith.science/paper/ZSUZ6CBU"},"agent_actions":{"view_html":"https://pith.science/pith/ZSUZ6CBUMICIT42RMRFJIXUKQ7","download_json":"https://pith.science/pith/ZSUZ6CBUMICIT42RMRFJIXUKQ7.json","view_paper":"https://pith.science/paper/ZSUZ6CBU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.1898&json=true","fetch_graph":"https://pith.science/api/pith-number/ZSUZ6CBUMICIT42RMRFJIXUKQ7/graph.json","fetch_events":"https://pith.science/api/pith-number/ZSUZ6CBUMICIT42RMRFJIXUKQ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZSUZ6CBUMICIT42RMRFJIXUKQ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZSUZ6CBUMICIT42RMRFJIXUKQ7/action/storage_attestation","attest_author":"https://pith.science/pith/ZSUZ6CBUMICIT42RMRFJIXUKQ7/action/author_attestation","sign_citation":"https://pith.science/pith/ZSUZ6CBUMICIT42RMRFJIXUKQ7/action/citation_signature","submit_replication":"https://pith.science/pith/ZSUZ6CBUMICIT42RMRFJIXUKQ7/action/replication_record"}},"created_at":"2026-05-18T02:26:51.754031+00:00","updated_at":"2026-05-18T02:26:51.754031+00:00"}