{"paper":{"title":"Detecting Model Misspecification in Bayesian Inverse Problems via Variational Gradient Descent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Comparing the standard Bayesian posterior to a predictively oriented mixing distribution detects model misspecification.","cross_cats":["stat.CO"],"primary_cat":"stat.ME","authors_text":"Andrew Curtis, Chris. J. Oates, Katherine Tant, Matthew A. Fisher, Qingyang Liu, Xuebin Zhao, Zheyang Shen","submitted_at":"2025-12-01T13:37:02Z","abstract_excerpt":"Bayesian inference is optimal when the statistical model is well-specified, while outside this setting Bayesian inference can catastrophically fail; accordingly a wealth of post-Bayesian methodologies have been proposed. Predictively oriented (PrO) approaches lift the statistical model $P_\\theta$ to an (infinite) mixture model $\\int P_\\theta \\; \\mathrm{d}Q(\\theta)$ and fit this predictive distribution via minimising an entropy-regularised objective functional. In the well-specified setting one expects the mixing distribution $Q$ to concentrate around the true data-generating parameter in the l"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our contribution is to demonstrate that one can empirically detect model misspecification by comparing the standard Bayesian posterior to the PrO `posterior' Q. To operationalise this, we present an efficient numerical algorithm based on variational gradient descent.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"In the well-specified setting one expects the mixing distribution Q to concentrate around the true data-generating parameter in the large data limit, while such singular concentration will typically not be observed if the model is misspecified.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Comparing the standard Bayesian posterior to a predictive-oriented mixture posterior Q fitted via variational gradient descent detects model misspecification in inverse problems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Comparing the standard Bayesian posterior to a predictively oriented mixing distribution detects model misspecification.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1854ac1b308944da4fdb5ac89b9a2017f8dff03d57c5b342a0723aa51de9be57"},"source":{"id":"2512.01667","kind":"arxiv","version":3},"verdict":{"id":"f99c6597-6cb3-4556-8b96-062fca4d3baf","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T02:54:47.786708Z","strongest_claim":"Our contribution is to demonstrate that one can empirically detect model misspecification by comparing the standard Bayesian posterior to the PrO `posterior' Q. To operationalise this, we present an efficient numerical algorithm based on variational gradient descent.","one_line_summary":"Comparing the standard Bayesian posterior to a predictive-oriented mixture posterior Q fitted via variational gradient descent detects model misspecification in inverse problems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"In the well-specified setting one expects the mixing distribution Q to concentrate around the true data-generating parameter in the large data limit, while such singular concentration will typically not be observed if the model is misspecified.","pith_extraction_headline":"Comparing the standard Bayesian posterior to a predictively oriented mixing distribution detects model misspecification."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.01667/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":2,"snapshot_sha256":"fea58772bfec07b005249e249d7725de12ba9450b397a2fc834301552a1d348a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}