{"paper":{"title":"Parametrized measure models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"H\\^ong V\\^an L\\^e, J\\\"urgen Jost, Lorenz Schwachh\\\"ofer, Nihat Ay","submitted_at":"2015-10-25T21:06:34Z","abstract_excerpt":"We develope a new and general notion of parametric measure models and statistical models on an arbitrary sample space $\\Omega$ which does not assume that all measures of the model have the same null sets. This is given by a diffferentiable map from the parameter manifold $M$ into the set of finite measures or probability measures on $\\Omega$, respectively, which is differentiable when regarded as a map into the Banach space of all signed measures on $\\Omega$. Furthermore, we also give a rigorous definition of roots of measures and give a natural definition of the Fisher metric and the Amari-Ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07305","kind":"arxiv","version":3},"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"}