{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:JQ3QTRLQUFVTH7V3K2XKBU5M2U","short_pith_number":"pith:JQ3QTRLQ","schema_version":"1.0","canonical_sha256":"4c3709c570a16b33febb56aea0d3acd53cfbaeba93aec3989a467457d2e8cd70","source":{"kind":"arxiv","id":"2312.07502","version":3},"attestation_state":"computed","paper":{"title":"Posterior Concentration for Gaussian Process Priors under Rescaled and Hierarchical Mat\\'ern and Confluent Hypergeometric Covariance Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Anindya Bhadra, Xiao Fang","submitted_at":"2023-12-12T18:35:31Z","abstract_excerpt":"In nonparameteric Bayesian approaches, Gaussian stochastic processes can serve as priors on real-valued function spaces. Existing literature on the posterior convergence rates under Gaussian process priors shows that it is possible to achieve optimal or near-optimal posterior contraction rates if the smoothness of the Gaussian process matches that of the target function. Among those priors, Gaussian processes with a parametric Mat\\'ern covariance function is particularly notable in that its degree of smoothness can be determined by a dedicated smoothness parameter. \\citet{ma2022beyond} recentl"},"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":"2312.07502","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-12-12T18:35:31Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"df458ea60ba146504f8cb81ff32c6dbcbc040d22a282fb87032b6e8f7dae081a","abstract_canon_sha256":"5ca5fbe011e593714c51f42393c7a6427e918ba97f208bd330adfff580c514bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:40.782235Z","signature_b64":"bFcXJ3JgHQyPSE6Fl+PGCBMfgn7K5FOLCCQ1kyEUpLGSG81BU+tMdIy2FfRVEd7kUaDsCqXKcNgQ9EqJzLxxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c3709c570a16b33febb56aea0d3acd53cfbaeba93aec3989a467457d2e8cd70","last_reissued_at":"2026-07-05T11:34:40.781763Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:40.781763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Posterior Concentration for Gaussian Process Priors under Rescaled and Hierarchical Mat\\'ern and Confluent Hypergeometric Covariance Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Anindya Bhadra, Xiao Fang","submitted_at":"2023-12-12T18:35:31Z","abstract_excerpt":"In nonparameteric Bayesian approaches, Gaussian stochastic processes can serve as priors on real-valued function spaces. Existing literature on the posterior convergence rates under Gaussian process priors shows that it is possible to achieve optimal or near-optimal posterior contraction rates if the smoothness of the Gaussian process matches that of the target function. Among those priors, Gaussian processes with a parametric Mat\\'ern covariance function is particularly notable in that its degree of smoothness can be determined by a dedicated smoothness parameter. \\citet{ma2022beyond} recentl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.07502","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.07502/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2312.07502","created_at":"2026-07-05T11:34:40.781830+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.07502v3","created_at":"2026-07-05T11:34:40.781830+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.07502","created_at":"2026-07-05T11:34:40.781830+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQ3QTRLQUFVT","created_at":"2026-07-05T11:34:40.781830+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQ3QTRLQUFVTH7V3","created_at":"2026-07-05T11:34:40.781830+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQ3QTRLQ","created_at":"2026-07-05T11:34:40.781830+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.24066","citing_title":"Adaptive Resolution for Finite-Rank Gaussian Processes","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U","json":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U.json","graph_json":"https://pith.science/api/pith-number/JQ3QTRLQUFVTH7V3K2XKBU5M2U/graph.json","events_json":"https://pith.science/api/pith-number/JQ3QTRLQUFVTH7V3K2XKBU5M2U/events.json","paper":"https://pith.science/paper/JQ3QTRLQ"},"agent_actions":{"view_html":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U","download_json":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U.json","view_paper":"https://pith.science/paper/JQ3QTRLQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.07502&json=true","fetch_graph":"https://pith.science/api/pith-number/JQ3QTRLQUFVTH7V3K2XKBU5M2U/graph.json","fetch_events":"https://pith.science/api/pith-number/JQ3QTRLQUFVTH7V3K2XKBU5M2U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/action/storage_attestation","attest_author":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/action/author_attestation","sign_citation":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/action/citation_signature","submit_replication":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/action/replication_record"}},"created_at":"2026-07-05T11:34:40.781830+00:00","updated_at":"2026-07-05T11:34:40.781830+00:00"}