{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:PWAXZKR5FQOHRLTGOYR6NSF5PM","short_pith_number":"pith:PWAXZKR5","schema_version":"1.0","canonical_sha256":"7d817caa3d2c1c78ae667623e6c8bd7b1ae9947109f86e0cd756f7db9f274719","source":{"kind":"arxiv","id":"2509.08834","version":1},"attestation_state":"computed","paper":{"title":"An Interval Type-2 Version of Bayes Theorem Derived from Interval Probability Range Estimates Provided by Subject Matter Experts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.comp-ph","physics.data-an","q-fin.CP"],"primary_cat":"cs.AI","authors_text":"James Rickards, John T. Rickard, William A. Dembski","submitted_at":"2025-08-29T23:47:31Z","abstract_excerpt":"Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to produce a precise output value. However, this is unrealistic for real-world applications. Often the best available information from subject matter experts (SMEs) in a given field is interval range estimates of the input probabilities involved in Bayes Theorem. This paper provides two key contributions to extend Bayes Theorem to an interval type-2 (IT2) version. First, we develop an IT2 version of Bayes Theorem that uses "},"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":"2509.08834","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2025-08-29T23:47:31Z","cross_cats_sorted":["physics.comp-ph","physics.data-an","q-fin.CP"],"title_canon_sha256":"a9a161f3bebba64144d6f8fc6afcc4d138846574475bc0925450f963374b94a4","abstract_canon_sha256":"a8fef9bd7b9398ab225bb6c77d5d1298fb8f4101e9b89a14d7b972f5aae07bb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:08:37.588795Z","signature_b64":"N4FSbr5VbE76TrUPYwCNcdRflP5FWgxN+fqyJ8IgJ7oArwAYxK6aZ1onBjS40I7zxKBXPGIeX5WlBsvXUdriBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d817caa3d2c1c78ae667623e6c8bd7b1ae9947109f86e0cd756f7db9f274719","last_reissued_at":"2026-07-05T12:08:37.588227Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:08:37.588227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Interval Type-2 Version of Bayes Theorem Derived from Interval Probability Range Estimates Provided by Subject Matter Experts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.comp-ph","physics.data-an","q-fin.CP"],"primary_cat":"cs.AI","authors_text":"James Rickards, John T. Rickard, William A. Dembski","submitted_at":"2025-08-29T23:47:31Z","abstract_excerpt":"Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to produce a precise output value. However, this is unrealistic for real-world applications. Often the best available information from subject matter experts (SMEs) in a given field is interval range estimates of the input probabilities involved in Bayes Theorem. This paper provides two key contributions to extend Bayes Theorem to an interval type-2 (IT2) version. First, we develop an IT2 version of Bayes Theorem that uses "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.08834","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.08834/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":"2509.08834","created_at":"2026-07-05T12:08:37.588283+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.08834v1","created_at":"2026-07-05T12:08:37.588283+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.08834","created_at":"2026-07-05T12:08:37.588283+00:00"},{"alias_kind":"pith_short_12","alias_value":"PWAXZKR5FQOH","created_at":"2026-07-05T12:08:37.588283+00:00"},{"alias_kind":"pith_short_16","alias_value":"PWAXZKR5FQOHRLTG","created_at":"2026-07-05T12:08:37.588283+00:00"},{"alias_kind":"pith_short_8","alias_value":"PWAXZKR5","created_at":"2026-07-05T12:08:37.588283+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/PWAXZKR5FQOHRLTGOYR6NSF5PM","json":"https://pith.science/pith/PWAXZKR5FQOHRLTGOYR6NSF5PM.json","graph_json":"https://pith.science/api/pith-number/PWAXZKR5FQOHRLTGOYR6NSF5PM/graph.json","events_json":"https://pith.science/api/pith-number/PWAXZKR5FQOHRLTGOYR6NSF5PM/events.json","paper":"https://pith.science/paper/PWAXZKR5"},"agent_actions":{"view_html":"https://pith.science/pith/PWAXZKR5FQOHRLTGOYR6NSF5PM","download_json":"https://pith.science/pith/PWAXZKR5FQOHRLTGOYR6NSF5PM.json","view_paper":"https://pith.science/paper/PWAXZKR5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.08834&json=true","fetch_graph":"https://pith.science/api/pith-number/PWAXZKR5FQOHRLTGOYR6NSF5PM/graph.json","fetch_events":"https://pith.science/api/pith-number/PWAXZKR5FQOHRLTGOYR6NSF5PM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PWAXZKR5FQOHRLTGOYR6NSF5PM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PWAXZKR5FQOHRLTGOYR6NSF5PM/action/storage_attestation","attest_author":"https://pith.science/pith/PWAXZKR5FQOHRLTGOYR6NSF5PM/action/author_attestation","sign_citation":"https://pith.science/pith/PWAXZKR5FQOHRLTGOYR6NSF5PM/action/citation_signature","submit_replication":"https://pith.science/pith/PWAXZKR5FQOHRLTGOYR6NSF5PM/action/replication_record"}},"created_at":"2026-07-05T12:08:37.588283+00:00","updated_at":"2026-07-05T12:08:37.588283+00:00"}