{"paper":{"title":"Posterior consistency and convergence rates for Bayesian inversion with hypoelliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Hanne Kekkonen, Matti Lassas, Samuli Siltanen","submitted_at":"2015-07-07T12:09:53Z","abstract_excerpt":"Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian random variable $U(x,\\omega)$ is \\begin{eqnarray*} M(y,\\omega) = A(U(x,\\omega) )+ \\delta\\hspace{.2mm}\\mathcal{E}(y,\\omega), \\end{eqnarray*} where $A$ is a finitely many times smoothing linear hypoelliptic operator and $\\delta>0$ is the noise magnitude. The covariance operator $C_U$ of $U$ is $2r$ times smoothing, self-adjoint, injective and elliptic pseudodiff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01772","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"}