TY  - JOUR
A1  - Helin, Tapio
A1  - Kretschmann, Remo
T1  - Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems
T2  - Numerische Mathematik
N2  - In this paper we study properties of the Laplace approximation of the posterior distribution arising in nonlinear Bayesian inverse problems. Our work is motivated by Schillings et al. (Numer Math 145:915–971, 2020. https://doi.org/10.1007/s00211-020-01131-1), where it is shown that in such a setting the Laplace approximation error in Hellinger distance converges to zero in the order of the noise level. Here, we prove novel error estimates for a given noise level that also quantify the effect due to the nonlinearity of the forward mapping and the dimension of the problem. In particular, we are interested in settings in which a linear forward mapping is perturbed by a small nonlinear mapping. Our results indicate that in this case, the Laplace approximation error is of the size of the perturbation. The paper provides insight into Bayesian inference in nonlinear inverse problems, where linearization of the forward mapping has suitable approximation properties.
KW  - Bayesian inverse problems
KW  - Laplace approximation
KW  - nonlinear inverse problems
Y1  - 2022
UR  - https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/26539
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-265399
VL  - 150
IS  - 2
ER  -