scholarly journals On the convergence of the Laplace approximation and noise-level-robustness of Laplace-based Monte Carlo methods for Bayesian inverse problems

2020 ◽  
Vol 145 (4) ◽  
pp. 915-971 ◽  
Author(s):  
Claudia Schillings ◽  
Björn Sprungk ◽  
Philipp Wacker
Keyword(s):  
Monte Carlo ◽  
Inverse Problems ◽  
Monte Carlo Methods ◽  
Noise Level ◽  
Laplace Approximation ◽  
Bayesian Inverse Problems

scholarly journals Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems

2022 ◽  
Author(s):  
Tapio Helin ◽  
Remo Kretschmann
Keyword(s):  
Inverse Problems ◽  
Error Estimates ◽  
Noise Level ◽  
Approximation Error ◽  
Laplace Approximation ◽  
Approximation Properties ◽  
Bayesian Inverse Problems ◽  
Numer Math ◽  
Forward Mapping ◽  
Suitable Approximation

AbstractIn 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. 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.

Use of perturbation and differential Monte Carlo methods to solve inverse problems in heterogeneous media

2004 ◽  
Author(s):  
Carole K. Hayakawa ◽  
Vanitha Sankaran ◽  
Frédéric Bevilacqua ◽  
Jerome Spanier ◽  
Vasan Venugopalan
Keyword(s):  
Monte Carlo ◽  
Inverse Problems ◽  
Monte Carlo Methods ◽  
Heterogeneous Media

scholarly journals Sequential Monte Carlo methods for Bayesian elliptic inverse problems

2015 ◽  
Vol 25 (4) ◽  
pp. 727-737 ◽  
Author(s):  
Alexandros Beskos ◽  
Ajay Jasra ◽  
Ege A. Muzaffer ◽  
Andrew M. Stuart
Keyword(s):  
Monte Carlo ◽  
Inverse Problems ◽  
Monte Carlo Methods ◽  
Sequential Monte Carlo ◽  
Sequential Monte Carlo Methods ◽  
Elliptic Inverse Problems

scholarly journals Multilevel Sequential2 Monte Carlo for Bayesian inverse problems

2018 ◽  
Vol 368 ◽  
pp. 154-178 ◽  
Author(s):  
Jonas Latz ◽  
Iason Papaioannou ◽  
Elisabeth Ullmann
Keyword(s):  
Monte Carlo ◽  
Inverse Problems ◽  
Bayesian Inverse Problems
Sign in / Sign up

Export Citation Format

Share Document