Hyperpriors for Matérn fields with applications in Bayesian inversion
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Publication:667766
DOI10.3934/ipi.2019001zbMath1454.60068arXiv1612.02989OpenAlexW2964007675MaRDI QIDQ667766
Markku Markkanen, Lassi Roininen, Sari Lasanen, Mark A. Girolami
Publication date: 1 March 2019
Published in: Inverse Problems and Imaging (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1612.02989
Random fields (60G60) Markov processes: estimation; hidden Markov models (62M05) Inverse problems in linear algebra (15A29) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)
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Uses Software
Cites Work
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- An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach
- Non-Gaussian statistical inverse problems. Part I: Posterior distributions
- A general framework for the parametrization of hierarchical models
- Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography
- Bayesian adaptive smoothing splines using stochastic differential equations
- Boundary value problems for the Laplacian in convex and semiconvex domains
- Statistical and computational inverse problems.
- Gaussian Markov random field priors for inverse problems
- Constructing continuous stationary covariances as limits of the second-order stochastic difference equations
- Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors
- Discretization-invariant Bayesian inversion and Besov space priors
- Cauchy difference priors for edge-preserving Bayesian inversion
- Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
- Inverse problems: A Bayesian perspective
- Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations
- Spatial Matérn Fields Driven by Non-Gaussian Noise
- Geostatistical Modelling Using Non-Gaussian Matérn Fields
- Algorithm 915, SuiteSparseQR
- Hierarchical models in statistical inverse problems and the Mumford–Shah functional
- Algorithm 933
- A Gaussian hypermodel to recover blocky objects
- Hypermodels in the Bayesian imaging framework
- How Deep Are Deep Gaussian Processes?
- Parameterizations for ensemble Kalman inversion
- Can one use total variation prior for edge-preserving Bayesian inversion?
- Gaussian Markov Random Fields
- Analysis of Finite Difference Schemes
- Introduction to Bayesian Scientific Computing
- MCMC methods for functions: modifying old algorithms to make them faster
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