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Remo Kretschmann (Universität Duisburg-Essen): Bayesian inverse problems with Laplacian noise

Wednesday, 25.01.2017 16:15
Mathematik und Informatik

Bayesian inverse problems with Laplacian noise We are interested in Bayesian inverse problems on function spaces with non-Gaussian noise. In the case of Gaussian noise and a Gaussian prior, MAP estimators can be characterised as minimisers of the Onsager-Machlup functional. We show that this connection also holds true for Laplacian noise. It provides a rigorous derivation of variational regularisations based upon explicit assumptions. Subsequently, we use this knowledge to study the inverse heat equation in a Bayesian setting with Laplacian noise and Gaussian prior. We make sure that a solution to the Bayesian inverse problem exists, determine its Onsager-Machlup functional and prove that the MAP estimator is consistent in a frequentist sense.



Angelegt am Friday, 23.12.2016 13:20 von wuebbel
Geändert am Monday, 16.01.2017 11:24 von wuebbel
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Oberseminar Angewandte Mathematik
Seminar AG Imaging