Ayanbayev, Birzhan and Klebanov, Ilja and Lie, Han Cheng and Sullivan, Timothy
*Γ-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems.*
Inverse Problems
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## Abstract

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 approach and by the Bayesian approach. To address this problem, we propose a general convergence theory for modes that is based on the Γ-convergence of Onsager-Machlup functionals, and apply this theory to Bayesian inverse problems with Gaussian and edge-preserving Besov priors. Part II of this paper considers more general prior distributions.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences > Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 2857 |

Deposited By: | BioComp Admin |

Deposited On: | 06 Jun 2023 15:42 |

Last Modified: | 06 Jun 2023 15:42 |

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