{"paper":{"title":"Propagating data noise through the fit: the Monte Carlo replica distribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Mark N. Costantini","submitted_at":"2026-06-26T18:00:03Z","abstract_excerpt":"The Monte Carlo (MC) replica method quantifies parameter uncertainties in global fits of parton distribution functions (PDFs) and Standard Model Effective Field Theory (SMEFT) Wilson coefficients by fitting a model to many noise-perturbed copies of the data and taking the empirical distribution of the best-fit parameters as the uncertainty. The method reproduces the Bayesian posterior exactly only when the model is linear in its parameters, and departs from it in the nonlinear case. We derive the leading-order distribution the method produces and compare it with the Laplace approximation of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28492","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/2606.28492/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"}