Corpus ID: 229153979

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

@article{Helin2020NonasymptoticEE,
  title={Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems},
  author={T. Helin and Remo Kretschmann},
  journal={ArXiv},
  year={2020},
  volume={abs/2012.06603}
}
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. (2020), 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… Expand
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SHOWING 1-10 OF 27 REFERENCES
On the convergence of the Laplace approximation and noise-level-robustness of Laplace-based Monte Carlo methods for Bayesian inverse problems
Multivariate Laplace's approximation with estimated error and application to limit theorems
Bernstein-von Mises Theorems and Uncertainty Quantification for Linear Inverse Problems
Error bounds for multidimensional Laplace approximation
Error bounds for the laplace approximation for definite integrals
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