{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:P2BQT37QM66XW4VGN4CFCCYYAP","short_pith_number":"pith:P2BQT37Q","schema_version":"1.0","canonical_sha256":"7e8309eff067bd7b72a66f04510b1803d8bdd7b23bef104b4318539437b79ef1","source":{"kind":"arxiv","id":"1411.6716","version":3},"attestation_state":"computed","paper":{"title":"Supremum Norm Posterior Contraction and Credible Sets for Nonparametric Multivariate Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Subhashis Ghosal, William Weimin Yoo","submitted_at":"2014-11-25T03:18:52Z","abstract_excerpt":"In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of tensor product of B-splines with normal basis coefficients as a prior for f, and the error variance is either estimated using the empirical Bayes approach or is endowed with a suitable prior in a hierarchical Bayes approach. We establish pointwise, L2 and supremum norm posterior contraction rates for f and its mixed partial derivatives, and show that they coinc"},"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":"1411.6716","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-11-25T03:18:52Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"560209cf6abdcb5e33c2d99a8ff3b1990c5dad9cecd1a101e10b7c7dc10b9b4b","abstract_canon_sha256":"4413e519101a4c2e723bfe0b82beec0868d79526d0b3c8e0de8895a4f97596db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:20.761971Z","signature_b64":"RGoKSYx1a1uXBTWVGegkNLmtXLBxEVHadcNlvf2EKT7wU/MqeyFVU/5/gP6vjcr3v7cM2pTaHS0lZsLCSEaAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e8309eff067bd7b72a66f04510b1803d8bdd7b23bef104b4318539437b79ef1","last_reissued_at":"2026-05-18T01:17:20.761359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:20.761359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Supremum Norm Posterior Contraction and Credible Sets for Nonparametric Multivariate Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Subhashis Ghosal, William Weimin Yoo","submitted_at":"2014-11-25T03:18:52Z","abstract_excerpt":"In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of tensor product of B-splines with normal basis coefficients as a prior for f, and the error variance is either estimated using the empirical Bayes approach or is endowed with a suitable prior in a hierarchical Bayes approach. We establish pointwise, L2 and supremum norm posterior contraction rates for f and its mixed partial derivatives, and show that they coinc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6716","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":"1411.6716","created_at":"2026-05-18T01:17:20.761444+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.6716v3","created_at":"2026-05-18T01:17:20.761444+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6716","created_at":"2026-05-18T01:17:20.761444+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2BQT37QM66X","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2BQT37QM66XW4VG","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2BQT37Q","created_at":"2026-05-18T12:28:43.426989+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/P2BQT37QM66XW4VGN4CFCCYYAP","json":"https://pith.science/pith/P2BQT37QM66XW4VGN4CFCCYYAP.json","graph_json":"https://pith.science/api/pith-number/P2BQT37QM66XW4VGN4CFCCYYAP/graph.json","events_json":"https://pith.science/api/pith-number/P2BQT37QM66XW4VGN4CFCCYYAP/events.json","paper":"https://pith.science/paper/P2BQT37Q"},"agent_actions":{"view_html":"https://pith.science/pith/P2BQT37QM66XW4VGN4CFCCYYAP","download_json":"https://pith.science/pith/P2BQT37QM66XW4VGN4CFCCYYAP.json","view_paper":"https://pith.science/paper/P2BQT37Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.6716&json=true","fetch_graph":"https://pith.science/api/pith-number/P2BQT37QM66XW4VGN4CFCCYYAP/graph.json","fetch_events":"https://pith.science/api/pith-number/P2BQT37QM66XW4VGN4CFCCYYAP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2BQT37QM66XW4VGN4CFCCYYAP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2BQT37QM66XW4VGN4CFCCYYAP/action/storage_attestation","attest_author":"https://pith.science/pith/P2BQT37QM66XW4VGN4CFCCYYAP/action/author_attestation","sign_citation":"https://pith.science/pith/P2BQT37QM66XW4VGN4CFCCYYAP/action/citation_signature","submit_replication":"https://pith.science/pith/P2BQT37QM66XW4VGN4CFCCYYAP/action/replication_record"}},"created_at":"2026-05-18T01:17:20.761444+00:00","updated_at":"2026-05-18T01:17:20.761444+00:00"}