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Modes of posterior measure for Bayesian inverse problems with a class of non-Gaussian priors

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UNQW04 - UQ for inverse problems in complex systems

We consider the inverse problem of recovering an unknown functional parameter from noisy and indirect observations. We adopt a Bayesian approach and, for a non-smooth, non-Gaussian and sparsity-promoting class of prior measures, show that maximum a posteriori (MAP) estimates are characterized by the minimizers of a generalized Onsager-Machlup functional of the posterior. We also discuss some posterior consistency results. This is based on joint works with S. Agapiou, M.Burger and T. Helin.

This talk is part of the Isaac Newton Institute Seminar Series series.

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