{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JN5JDLUGVCEMRCZDP7CQMC57OX","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":"c6df3c0c06277422ad50b81bd997245052aa2f1bad61647939e61c8fbf06401f","cross_cats_sorted":["quant-ph","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-06T20:47:37Z","title_canon_sha256":"d705973db8c413a24b088494f78c9d894b90334acdc28828554ec8215f2be29b"},"schema_version":"1.0","source":{"id":"1201.1493","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1493","created_at":"2026-05-18T02:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1493v1","created_at":"2026-05-18T02:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1493","created_at":"2026-05-18T02:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"JN5JDLUGVCEM","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JN5JDLUGVCEMRCZD","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JN5JDLUG","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:5face455b04e5e1991471f289289c3f844e4931fce4b36c0f8e3d2c530294dfd","target":"graph","created_at":"2026-05-18T02:21:18Z","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":"Optimal estimation of a coin's bias using noisy data is surprisingly different from the same problem with noiseless data. We study this problem using entropy risk to quantify estimators' accuracy. We generalize the \"add Beta\" estimators that work well for noiseless coins, and we find that these hedged maximum-likelihood (HML) estimators achieve a worst-case risk of O(N^{-1/2}) on noisy coins, in contrast to O(1/N) in the noiseless case. We demonstrate that this increased risk is unavoidable and intrinsic to noisy coins, by constructing minimax estimators (numerically). However, minimax estimat","authors_text":"Christopher Ferrie, Robin Blume-Kohout","cross_cats":["quant-ph","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-06T20:47:37Z","title":"Estimating the bias of a noisy coin"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1493","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":"sha256:4996bc7805812c08de2402fe1663f4e6fb149dc1bf1b0da3db49e8b62486e811","target":"record","created_at":"2026-05-18T02:21:18Z","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":"c6df3c0c06277422ad50b81bd997245052aa2f1bad61647939e61c8fbf06401f","cross_cats_sorted":["quant-ph","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-06T20:47:37Z","title_canon_sha256":"d705973db8c413a24b088494f78c9d894b90334acdc28828554ec8215f2be29b"},"schema_version":"1.0","source":{"id":"1201.1493","kind":"arxiv","version":1}},"canonical_sha256":"4b7a91ae86a888c88b237fc5060bbf75da0d6f29e1ab9f8fae919b6e6ed34aec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b7a91ae86a888c88b237fc5060bbf75da0d6f29e1ab9f8fae919b6e6ed34aec","first_computed_at":"2026-05-18T02:21:18.850696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:18.850696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e1THO1yPjr0wMPJSWkfrQe/E9veyiijxWnLUxnMCQDifjU0UnY9eTnjE6bCcSnXY3NbN/c7dD6iv2y/NBtHZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:18.851345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1493","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4996bc7805812c08de2402fe1663f4e6fb149dc1bf1b0da3db49e8b62486e811","sha256:5face455b04e5e1991471f289289c3f844e4931fce4b36c0f8e3d2c530294dfd"],"state_sha256":"cdcad5e5687f0144a90f10200cc7bf156adab96d5eacc5b210c07a252d537a84"}