{"paper":{"title":"Sensitivity analysis for multidimensional and functional outputs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.ME","stat.TH"],"primary_cat":"stat.AP","authors_text":"Agn\\`es Lagnoux (IMT), Alexandre Janon (LM-Orsay, Fabrice Gamboa (UMR CNRS 5219), - M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques), Thierry Klein (IMT)","submitted_at":"2013-11-07T20:09:54Z","abstract_excerpt":"Let $X:=(X_1, \\ldots, X_p)$ be random objects (the inputs), defined on some probability space $(\\Omega,{\\mathcal{F}}, \\mathbb P)$ and valued in some measurable space $E=E_1\\times\\ldots \\times E_p$. Further, let $Y:=Y = f(X_1, \\ldots, X_p)$ be the output. Here, $f$ is a measurable function from $E$ to some Hilbert space $\\mathbb{H}$ ($\\mathbb{H}$ could be either of finite or infinite dimension). In this work, we give a natural generalization of the Sobol indices (that are classically defined when $Y\\in\\mathbb R$ ), when the output belongs to $\\mathbb{H}$. These indices have very nice properties"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1797","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}