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

Presented by: 
Masoumeh Dashti University of Sussex
Thursday 12th April 2018 - 10:00 to 10:30
INI Seminar Room 1
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.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons