{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GUVD2JL7AI3GWP6C3WJX25XDAO","short_pith_number":"pith:GUVD2JL7","schema_version":"1.0","canonical_sha256":"352a3d257f02366b3fc2dd937d76e30396bb0d6dc86d7963970381d77f070505","source":{"kind":"arxiv","id":"2606.07169","version":1},"attestation_state":"computed","paper":{"title":"When can a posterior predictive check identify the learning rate? Exact degeneracy in Gaussian models and implications for Generalised Bayesian Inerence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Nam Anh Le","submitted_at":"2026-06-05T11:38:48Z","abstract_excerpt":"Generalised Bayesian inference tempers the likelihood by a learning rate $\\eta$ to mitigate model misspecification, and the choice of $\\eta$ is consequential. Zafar and Nicholls (2024) proposed selecting $\\eta$ by a posterior predictive check (PPC): one chooses the smallest $\\eta$ at which a log-likelihood PPC $p$-value is not rejected. An exact, finite-sample analysis of this selector on the Gaussian linear model is given. With known variance and a flat prior, the PPC $p$-value equals $P(\\chi^2_n > \\mathrm{RSS}/\\sigma_0^2)$ for every $\\eta$, so the selector is $\\eta$-invariant; under variance"},"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":"2606.07169","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-06-05T11:38:48Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"b4fd6d44fc3b17298489fea4635bd2dc38bb04c5ca6eefa1a1d853414e239663","abstract_canon_sha256":"cb9fbd629db4cfc3e37ad01fb5ce12118bc485d3ede1315fb61a9e3abd16c5b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:04:50.464435Z","signature_b64":"DHjMUaX6O8yvivXnOStrCvYFFcGxdfkDmmRhUGodRx3DH9ca7QtuchtMrtAefPkrIKp2ee9pn9/Pcf5fy4OpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"352a3d257f02366b3fc2dd937d76e30396bb0d6dc86d7963970381d77f070505","last_reissued_at":"2026-06-08T01:04:50.463578Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:04:50.463578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When can a posterior predictive check identify the learning rate? Exact degeneracy in Gaussian models and implications for Generalised Bayesian Inerence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Nam Anh Le","submitted_at":"2026-06-05T11:38:48Z","abstract_excerpt":"Generalised Bayesian inference tempers the likelihood by a learning rate $\\eta$ to mitigate model misspecification, and the choice of $\\eta$ is consequential. Zafar and Nicholls (2024) proposed selecting $\\eta$ by a posterior predictive check (PPC): one chooses the smallest $\\eta$ at which a log-likelihood PPC $p$-value is not rejected. An exact, finite-sample analysis of this selector on the Gaussian linear model is given. With known variance and a flat prior, the PPC $p$-value equals $P(\\chi^2_n > \\mathrm{RSS}/\\sigma_0^2)$ for every $\\eta$, so the selector is $\\eta$-invariant; under variance"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07169","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/2606.07169/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":"2606.07169","created_at":"2026-06-08T01:04:50.463718+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.07169v1","created_at":"2026-06-08T01:04:50.463718+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07169","created_at":"2026-06-08T01:04:50.463718+00:00"},{"alias_kind":"pith_short_12","alias_value":"GUVD2JL7AI3G","created_at":"2026-06-08T01:04:50.463718+00:00"},{"alias_kind":"pith_short_16","alias_value":"GUVD2JL7AI3GWP6C","created_at":"2026-06-08T01:04:50.463718+00:00"},{"alias_kind":"pith_short_8","alias_value":"GUVD2JL7","created_at":"2026-06-08T01:04:50.463718+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/GUVD2JL7AI3GWP6C3WJX25XDAO","json":"https://pith.science/pith/GUVD2JL7AI3GWP6C3WJX25XDAO.json","graph_json":"https://pith.science/api/pith-number/GUVD2JL7AI3GWP6C3WJX25XDAO/graph.json","events_json":"https://pith.science/api/pith-number/GUVD2JL7AI3GWP6C3WJX25XDAO/events.json","paper":"https://pith.science/paper/GUVD2JL7"},"agent_actions":{"view_html":"https://pith.science/pith/GUVD2JL7AI3GWP6C3WJX25XDAO","download_json":"https://pith.science/pith/GUVD2JL7AI3GWP6C3WJX25XDAO.json","view_paper":"https://pith.science/paper/GUVD2JL7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.07169&json=true","fetch_graph":"https://pith.science/api/pith-number/GUVD2JL7AI3GWP6C3WJX25XDAO/graph.json","fetch_events":"https://pith.science/api/pith-number/GUVD2JL7AI3GWP6C3WJX25XDAO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GUVD2JL7AI3GWP6C3WJX25XDAO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GUVD2JL7AI3GWP6C3WJX25XDAO/action/storage_attestation","attest_author":"https://pith.science/pith/GUVD2JL7AI3GWP6C3WJX25XDAO/action/author_attestation","sign_citation":"https://pith.science/pith/GUVD2JL7AI3GWP6C3WJX25XDAO/action/citation_signature","submit_replication":"https://pith.science/pith/GUVD2JL7AI3GWP6C3WJX25XDAO/action/replication_record"}},"created_at":"2026-06-08T01:04:50.463718+00:00","updated_at":"2026-06-08T01:04:50.463718+00:00"}