Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography
By Lassi Roininen, Janne M. J. Huttunen, Sari Lasanen. 2014
140 citations recorded by the source corpus.
We study flexible and proper smoothness priors for Bayesian statistical inverse problems by using Whittle-Matern Gaussian random fields. We review earlier results on finite-difference approximations of certain Whittle-Matern random field in $\mathbb{R}^2$. Then we derive finite-element method approximations and show that the discrete approximations can be expressed as solutions of sparse stochastic matrix equations. Such equations are known to be computationally efficient and useful in inverse problems with a large number of unknowns. The presented construction of Whittle-Matern correlation functions allows both isotropic or anisotropic priors with adjustable parameters in correlation length and variance. These parameters can be used, for example, to model spatially varying structural information of unknowns. As numerical examples, we apply the developed priors to two-dimensional electrical impedance tomography problems.
Subfields: Electrical and Electronic Engineering, Geophysics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a562a5c5cb034373dd2796d5ecc2fadcface6a9c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Electrical and Electronic Engineering
In Geophysics
In Statistics and Probability
- Gabriel P. Paternain
- F. Monard
- Lassi Roininen
- Richard Nickl
- Sari Lasanen
- M. Markkanen
- Mark A. Girolami
- Kolyan Ray
Citations in the corpus
- Statistical guarantees for Bayesian uncertainty quantification in nonlinear inverse problems with Gaussian process priors (2020, methodology): “While these measures of uncertainty can be computed by MCMC methods (see [32, 33, 13, 54, 12, 5] and below), few statistical guarantees are available for the validity of such posterior inferences in typical PDE settings where G is non-linear and θ is modelled as a Gaussian process.”
- Hyperpriors for Matérn fields with applications in Bayesian inversion (2016, background): “Let us recall the stochastic partial differential equation for the Matérn fields [25, 32].”