{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:SLKKMT7OA6EWLDEECU3Y4AMTP7","short_pith_number":"pith:SLKKMT7O","schema_version":"1.0","canonical_sha256":"92d4a64fee0789658c8415378e01937ff7668e7b86ab58d3d3f74f3580c4cd2e","source":{"kind":"arxiv","id":"1906.01204","version":1},"attestation_state":"computed","paper":{"title":"Robust Mean Estimation with the Bayesian Median of Means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Paulo Orenstein","submitted_at":"2019-06-04T05:41:52Z","abstract_excerpt":"The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that roughly interpolates between the sample mean and median, resulting in estimates with much smaller variance at the expense of bias. While the procedure is non-parametric, its squared bias is asymptotically negligible relative to the variance, similar to maximum likelihood estimators. The Bayesian median of means is consistent, and concentration bounds for the es"},"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":"1906.01204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-06-04T05:41:52Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"001f23e109e89c7756cc81faf25f0f4c67c4de2dd12be1cf71c50041dea08f3c","abstract_canon_sha256":"f67ffae6bcb1f297a781474f11125718177ff438db4207cf222f0efcea423531"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:17.537401Z","signature_b64":"KA7kOqeET9TeCm952visHEIY9qhoBpnoYN+1FTOdoYGMsNEmxtacSJStUzHBLHCULw53v1jyd1HX3zA4YdNHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92d4a64fee0789658c8415378e01937ff7668e7b86ab58d3d3f74f3580c4cd2e","last_reissued_at":"2026-05-17T23:44:17.536660Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:17.536660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Robust Mean Estimation with the Bayesian Median of Means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Paulo Orenstein","submitted_at":"2019-06-04T05:41:52Z","abstract_excerpt":"The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that roughly interpolates between the sample mean and median, resulting in estimates with much smaller variance at the expense of bias. While the procedure is non-parametric, its squared bias is asymptotically negligible relative to the variance, similar to maximum likelihood estimators. The Bayesian median of means is consistent, and concentration bounds for the es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01204","kind":"arxiv","version":1},"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":"1906.01204","created_at":"2026-05-17T23:44:17.536786+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.01204v1","created_at":"2026-05-17T23:44:17.536786+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01204","created_at":"2026-05-17T23:44:17.536786+00:00"},{"alias_kind":"pith_short_12","alias_value":"SLKKMT7OA6EW","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"SLKKMT7OA6EWLDEE","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"SLKKMT7O","created_at":"2026-05-18T12:33:27.125529+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/SLKKMT7OA6EWLDEECU3Y4AMTP7","json":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7.json","graph_json":"https://pith.science/api/pith-number/SLKKMT7OA6EWLDEECU3Y4AMTP7/graph.json","events_json":"https://pith.science/api/pith-number/SLKKMT7OA6EWLDEECU3Y4AMTP7/events.json","paper":"https://pith.science/paper/SLKKMT7O"},"agent_actions":{"view_html":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7","download_json":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7.json","view_paper":"https://pith.science/paper/SLKKMT7O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.01204&json=true","fetch_graph":"https://pith.science/api/pith-number/SLKKMT7OA6EWLDEECU3Y4AMTP7/graph.json","fetch_events":"https://pith.science/api/pith-number/SLKKMT7OA6EWLDEECU3Y4AMTP7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/action/storage_attestation","attest_author":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/action/author_attestation","sign_citation":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/action/citation_signature","submit_replication":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/action/replication_record"}},"created_at":"2026-05-17T23:44:17.536786+00:00","updated_at":"2026-05-17T23:44:17.536786+00:00"}