{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:FDQC7XLA4UQWZN76PK3LHPGLDX","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":"fcaa56399521e3425f4cb6e4ad63b0630505af6fd772dcbab30fd10b21c7c067","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2008-07-01T01:33:17Z","title_canon_sha256":"4d89687a99019cdd470d3942df2ce23d6d7e629e3474940e65969f71cf490edb"},"schema_version":"1.0","source":{"id":"0807.0053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.0053","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"0807.0053v1","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.0053","created_at":"2026-05-18T03:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"FDQC7XLA4UQW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"FDQC7XLA4UQWZN76","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"FDQC7XLA","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:498c0ca98ce9163c8a29e7d42f02ed9f268d1f926248c7fe2f9b1862f895a937","target":"graph","created_at":"2026-05-18T03:04:07Z","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":"A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is represented as an arbitrary-shaped region. We introduce new parametric models for the scaling-law of bootstrap probability so that the multiscale bootstrap method, which was designed for one-sided test, can also computes confidence measures of two-sided test, extending applicability to a wider class of hypotheses. Parameter estimation is improved by the two-step","authors_text":"Hidetoshi Shimodaira","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2008-07-01T01:33:17Z","title":"Frequentist and Bayesian measures of confidence via multiscale bootstrap for testing three regions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0053","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":"sha256:265b7a04352909a90da334e67af7238cbb486cc10ff1290db4127355deb3f809","target":"record","created_at":"2026-05-18T03:04:07Z","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":"fcaa56399521e3425f4cb6e4ad63b0630505af6fd772dcbab30fd10b21c7c067","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2008-07-01T01:33:17Z","title_canon_sha256":"4d89687a99019cdd470d3942df2ce23d6d7e629e3474940e65969f71cf490edb"},"schema_version":"1.0","source":{"id":"0807.0053","kind":"arxiv","version":1}},"canonical_sha256":"28e02fdd60e5216cb7fe7ab6b3bccb1df943b316b3a5b9abe46cf29657421dcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28e02fdd60e5216cb7fe7ab6b3bccb1df943b316b3a5b9abe46cf29657421dcd","first_computed_at":"2026-05-18T03:04:07.086141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:07.086141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dfi77chVcIQT8E8IbRuypJhzOB4/4WjR7Jm60zteHaEE3LZjq/hoYa4oXQC6VE/aNEnrYLyJ1se+VdlDO8FSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:07.086635Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.0053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:265b7a04352909a90da334e67af7238cbb486cc10ff1290db4127355deb3f809","sha256:498c0ca98ce9163c8a29e7d42f02ed9f268d1f926248c7fe2f9b1862f895a937"],"state_sha256":"7ff2c3c0bff5a21eb79eb1245b2a7a9d427819495a41858f8c3a59a33ab005f6"}