{"paper":{"title":"Multilevel randomized quasi-Monte Carlo estimator for nested integration","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Andr\\'e Gustavo Carlon, Arved Bartuska, Luis Espath, Ra\\'ul Tempone, Sebastian Krumscheid","submitted_at":"2024-12-10T18:16:25Z","abstract_excerpt":"Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\\int f\\left(\\int g(\\boldsymbol{y},\\boldsymbol{x})\\mathrm{d}\\boldsymbol{x}\\right)\\mathrm{d}\\boldsymbol{y}$, for nonlinear $f$, making them computationally challenging, particularly in high-dimensional settings. Although widely used for single integrals, traditional Monte Carlo (MC) methods can be inefficient when encountering complexities of nested integration. This work intr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.07723","kind":"arxiv","version":5},"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/2412.07723/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"}