{"paper":{"title":"MAP Estimators and Their Consistency in Bayesian Nonparametric Inverse Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew M. Stuart, Jochen Voss, Kody J. H. Law, Masoumeh Dashti","submitted_at":"2013-03-20T00:01:41Z","abstract_excerpt":"We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the prior measure is specified as a Gaussian random field $\\mu_0$. We work under a natural set of conditions on the likelihood which imply the existence of a well-posed posterior measure, $\\mu^y$. Under these conditions we show that the {\\em maximum a posteriori} (MAP) estimator is well-defined as the minimiser of an Onsager-Machlup functional defined on the Cam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4795","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"}