TY  - JOUR
A1  - Ayanbayev, Birzhan
A1  - Klebanov, Ilja
A1  - Li, Han Cheng
A1  - Sullivan, Tim J.
T1  - Gamma-convergence of Onsager-Machlup functionals
T2  - Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data
N2  - The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a maximum a posteriori (MAP) estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse problem, seen as minimisation of the Onsager-Machlup (OM) 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 Gamma-convergence of OM 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.
KW  - Bayesian inverse problems
KW  - Gamma-convergence
KW  - maximum a posteriori
KW  - estimation
KW  - Onsager-Machlup functional
KW  - small ball probabilities;
KW  - transition path theory
Y1  - 2021
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/62336
SN  - 0266-5611
SN  - 1361-6420
VL  - 38
IS  - 2
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -