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# \Gamma-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems

@inproceedings{Ayanbayev2021GammaconvergenceOO,
title={\Gamma-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems},
author={Birzhan Ayanbayev and I. Klebanov and H. Lie and T. Sullivan},
year={2021}
}
The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a MAP estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse problem, seen as minimisation of the Onsager–Machlup functional of the posterior measure. An open problem in the stability analysis of inverse problems is to establish a relationship between the convergence properties of solutions obtained by the variational… Expand

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