Numerical realization of the Bayesian inversion accelerated using surrogate models

Bérešová, Simona. "Numerical realization of the Bayesian inversion accelerated using surrogate models." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2023. 25-36. <http://eudml.org/doc/299008>.

@inProceedings{Bérešová2023,
abstract = {The Bayesian inversion is a natural approach to the solution of inverse problems based on uncertain observed data. The result of such an inverse problem is the posterior distribution of unknown parameters. This paper deals with the numerical realization of the Bayesian inversion focusing on problems governed by computationally expensive forward models such as numerical solutions of partial differential equations. Samples from the posterior distribution are generated using the Markov chain Monte Carlo (MCMC) methods accelerated with surrogate models. A surrogate model is understood as an approximation of the forward model which should be computationally much cheaper. The target distribution is not fully replaced by its approximation; therefore, samples from the exact posterior distribution are provided. In addition, non-intrusive surrogate models can be updated during the sampling process resulting in an adaptive MCMC method. The use of the surrogate models significantly reduces the number of evaluations of the forward model needed for a reliable description of the posterior distribution. Described sampling procedures are implemented in the form of a Python package.},
author = {Bérešová, Simona},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {Bayesian inversion; delayed-acceptance Metropolis-Hastings; Markov chain Monte Carlo; surrogate model},
location = {Prague},
pages = {25-36},
publisher = {Institute of Mathematics CAS},
title = {Numerical realization of the Bayesian inversion accelerated using surrogate models},
url = {http://eudml.org/doc/299008},
year = {2023},
}

TY - CLSWK
AU - Bérešová, Simona
TI - Numerical realization of the Bayesian inversion accelerated using surrogate models
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2023
CY - Prague
PB - Institute of Mathematics CAS
SP - 25
EP - 36
AB - The Bayesian inversion is a natural approach to the solution of inverse problems based on uncertain observed data. The result of such an inverse problem is the posterior distribution of unknown parameters. This paper deals with the numerical realization of the Bayesian inversion focusing on problems governed by computationally expensive forward models such as numerical solutions of partial differential equations. Samples from the posterior distribution are generated using the Markov chain Monte Carlo (MCMC) methods accelerated with surrogate models. A surrogate model is understood as an approximation of the forward model which should be computationally much cheaper. The target distribution is not fully replaced by its approximation; therefore, samples from the exact posterior distribution are provided. In addition, non-intrusive surrogate models can be updated during the sampling process resulting in an adaptive MCMC method. The use of the surrogate models significantly reduces the number of evaluations of the forward model needed for a reliable description of the posterior distribution. Described sampling procedures are implemented in the form of a Python package.
KW - Bayesian inversion; delayed-acceptance Metropolis-Hastings; Markov chain Monte Carlo; surrogate model
UR - http://eudml.org/doc/299008
ER -