{"paper":{"title":"Maximum-A-Posteriori Estimates in Linear Inverse Problems with Log-concave Priors are Proper Bayes Estimators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Felix Lucka, Martin Burger","submitted_at":"2014-02-21T13:53:54Z","abstract_excerpt":"A frequent matter of debate in Bayesian inversion is the question, which of the two principle point-estimators, the maximum-a-posteriori (MAP) or the conditional mean (CM) estimate is to be preferred. As the MAP estimate corresponds to the solution given by variational regularization techniques, this is also a constant matter of debate between the two research areas. Following a theoretical argument - the Bayes cost formalism - the CM estimate is classically preferred for being the Bayes estimator for the mean squared error cost while the MAP estimate is classically discredited for being only "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5297","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"}