Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo
DOI10.1137/20M1349606zbMath1467.62155arXiv2007.14440OpenAlexW3172807751MaRDI QIDQ4997424
Hillary R. Fairbanks, Umberto Villa, Panayot S. Vassilevski
Publication date: 29 June 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.14440
Markov chain Monte Carloalgebraic multigridGaussian random fieldhigh-dimensional uncertainty quantificationmultilevel Markov chain Monte Carlononlinear Bayesian inference
Computational methods for problems pertaining to statistics (62-08) Inference from spatial processes (62M30) Numerical analysis or methods applied to Markov chains (65C40) PDEs with randomness, stochastic partial differential equations (35R60)
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
- Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients
- Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
- Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography
- Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
- Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
- Geometric MCMC for infinite-dimensional inverse problems
- Mitigating the influence of the boundary on PDE-based covariance operators
- MFEM: a modular finite element methods library
- Dimension-independent likelihood-informed MCMC
- Inverse problems: A Bayesian perspective
- A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
- Multilevel Monte Carlo Methods
- Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo
- Likelihood-informed dimension reduction for nonlinear inverse problems
- Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations
- Multilevel Monte Carlo Path Simulation
- A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow
- An overview of the Trilinos project
- Analysis of Circulant Embedding Methods for Sampling Stationary Random Fields
- Efficient White Noise Sampling and Coupling for Multilevel Monte Carlo with Nonnested Meshes
- Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes
- Analysis of a multilevel Markov chain Monte Carlo finite element method for Bayesian inversion of log-normal diffusions
- Equation of State Calculations by Fast Computing Machines
- Algebraic Hybridization and Static Condensation with Application to Scalable $H$(div) Preconditioning
- Analysis of Boundary Effects on PDE-Based Sampling of Whittle--Matérn Random Fields
- Parallel Solver for $$\boldsymbol{H}$$ (div) Problems Using Hybridization and AMG
- Random Fields and Geometry
- A Bayesian approach to characterizing uncertainty in inverse problems using coarse and fine-scale information
- A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields
- Scheduling Massively Parallel Multigrid for Multilevel Monte Carlo Methods
- A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion
- Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models
- Monte Carlo sampling methods using Markov chains and their applications
- MCMC methods for functions: modifying old algorithms to make them faster
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