DeepAI
Log In Sign Up

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

12/11/2020
by   Tapio Helin, et al.
0

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 the problem. In particular, we are interested in inverse problems, where 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/15/2017

Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems

This paper develops meshless methods for probabilistically describing di...
12/29/2019

Bayesian inference for nonlinear inverse problems

Bayesian methods are actively used for parameter identification and unce...
11/30/2021

Bayesian Level Set Approach for Inverse Problems with Piecewise Constant Reconstructions

There are several challenges associated with inverse problems in which w...
01/24/2023

Sequential model correction for nonlinear inverse problems

Inverse problems are in many cases solved with optimization techniques. ...
07/02/2018

Certified dimension reduction in nonlinear Bayesian inverse problems

We propose a dimension reduction technique for Bayesian inverse problems...
06/01/2021

Consensus Based Sampling

We propose a novel method for sampling and optimization tasks based on a...
01/26/2020

Solving Laplace problems with the AAA algorithm

We present a novel application of the recently developed AAA algorithm t...