{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SLKKMT7OA6EWLDEECU3Y4AMTP7","short_pith_number":"pith:SLKKMT7O","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"},"canonical_sha256":"92d4a64fee0789658c8415378e01937ff7668e7b86ab58d3d3f74f3580c4cd2e","source":{"kind":"arxiv","id":"1906.01204","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01204","created_at":"2026-05-17T23:44:17Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01204v1","created_at":"2026-05-17T23:44:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01204","created_at":"2026-05-17T23:44:17Z"},{"alias_kind":"pith_short_12","alias_value":"SLKKMT7OA6EW","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SLKKMT7OA6EWLDEE","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SLKKMT7O","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SLKKMT7OA6EWLDEECU3Y4AMTP7","target":"record","payload":{"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"},"canonical_sha256":"92d4a64fee0789658c8415378e01937ff7668e7b86ab58d3d3f74f3580c4cd2e","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"},"source_kind":"arxiv","source_id":"1906.01204","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MubBx0OPeYTIKA3XwbRYD+p74y8clOiimCPm1cCgnatRWnJiWgksPkw9+m1yxId1FhHfHIvBBPZWCuYNo9LvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:59:50.744497Z"},"content_sha256":"2f127f92bcb382a534698d260221281e80f59fc3286ddd6cf59772a19d82aab2","schema_version":"1.0","event_id":"sha256:2f127f92bcb382a534698d260221281e80f59fc3286ddd6cf59772a19d82aab2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SLKKMT7OA6EWLDEECU3Y4AMTP7","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e7P0nvgzok+HVAoPRUdQxH/I4sfbQkbcyk94AAbZUn+c/wkqfusu/SZKfaiXV2Gj/wi+BqNvaVIXXtOKdhjNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:59:50.745213Z"},"content_sha256":"4caaedc0dec2345b5225707eb9493b83c2cfe59302aaf7d509033fc42036d15e","schema_version":"1.0","event_id":"sha256:4caaedc0dec2345b5225707eb9493b83c2cfe59302aaf7d509033fc42036d15e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/bundle.json","state_url":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T16:59:50Z","links":{"resolver":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7","bundle":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/bundle.json","state":"https://pith.science/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SLKKMT7OA6EWLDEECU3Y4AMTP7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SLKKMT7OA6EWLDEECU3Y4AMTP7","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":"f67ffae6bcb1f297a781474f11125718177ff438db4207cf222f0efcea423531","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-06-04T05:41:52Z","title_canon_sha256":"001f23e109e89c7756cc81faf25f0f4c67c4de2dd12be1cf71c50041dea08f3c"},"schema_version":"1.0","source":{"id":"1906.01204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01204","created_at":"2026-05-17T23:44:17Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01204v1","created_at":"2026-05-17T23:44:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01204","created_at":"2026-05-17T23:44:17Z"},{"alias_kind":"pith_short_12","alias_value":"SLKKMT7OA6EW","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SLKKMT7OA6EWLDEE","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SLKKMT7O","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:4caaedc0dec2345b5225707eb9493b83c2cfe59302aaf7d509033fc42036d15e","target":"graph","created_at":"2026-05-17T23:44:17Z","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 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","authors_text":"Paulo Orenstein","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-06-04T05:41:52Z","title":"Robust Mean Estimation with the Bayesian Median of Means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01204","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":"sha256:2f127f92bcb382a534698d260221281e80f59fc3286ddd6cf59772a19d82aab2","target":"record","created_at":"2026-05-17T23:44:17Z","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":"f67ffae6bcb1f297a781474f11125718177ff438db4207cf222f0efcea423531","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-06-04T05:41:52Z","title_canon_sha256":"001f23e109e89c7756cc81faf25f0f4c67c4de2dd12be1cf71c50041dea08f3c"},"schema_version":"1.0","source":{"id":"1906.01204","kind":"arxiv","version":1}},"canonical_sha256":"92d4a64fee0789658c8415378e01937ff7668e7b86ab58d3d3f74f3580c4cd2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92d4a64fee0789658c8415378e01937ff7668e7b86ab58d3d3f74f3580c4cd2e","first_computed_at":"2026-05-17T23:44:17.536660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:17.536660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KA7kOqeET9TeCm952visHEIY9qhoBpnoYN+1FTOdoYGMsNEmxtacSJStUzHBLHCULw53v1jyd1HX3zA4YdNHBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:17.537401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.01204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f127f92bcb382a534698d260221281e80f59fc3286ddd6cf59772a19d82aab2","sha256:4caaedc0dec2345b5225707eb9493b83c2cfe59302aaf7d509033fc42036d15e"],"state_sha256":"59fdde35e13a79828be23b4b88e07237c07469f0f8f72986d3d435ba7dfbac24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ctzdf0/QvLx3wEe3g2w6QdpcAi9wtlFJFQF0J2Ezld4KL2nP7P7R88dmMEPtacy2BQq3XRi4cfqFYvQzRS+7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:59:50.749294Z","bundle_sha256":"678bea0c0cd181fd35df97758bda7a11a52048329c579cc0f10b309155df9fbc"}}