A Randomized Maximum A Posteriori Method for Posterior Sampling of High Dimensional Nonlinear Bayesian Inverse Problems
From MaRDI portal
Publication:3130408
DOI10.1137/16M1060625zbMath1386.35391arXiv1602.03658OpenAlexW2268335277MaRDI QIDQ3130408
Tan Bui-Thanh, Kainan Wang, Omar Ghattas
Publication date: 22 January 2018
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1602.03658
inverse problemsMarkov chain Monte Carlouncertainty quantificationrandomized maximum a posterioritrust region inexact Newton conjugate gradient
Bayesian inference (62F15) Inverse problems for PDEs (35R30) PDEs in connection with control and optimization (35Q93) PDEs in connection with statistics (35Q62)
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Cites Work
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- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- FEM-based discretization-invariant MCMC methods for PDE-constrained Bayesian inverse problems
- Minimization for conditional simulation: relationship to optimal transport
- Hybrid Monte Carlo on Hilbert spaces
- Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the antarctic ice sheet
- Exponential convergence of Langevin distributions and their discrete approximations
- Large-scale PDE-constrained optimization
- Evaluation of Gaussian approximations for data assimilation in reservoir models
- Statistical and computational inverse problems.
- Dimension-independent likelihood-informed MCMC
- Analysis of the Hessian for inverse scattering problems. III: Inverse medium scattering of electromagnetic waves in three dimensions.
- Efficient parallelisation of Metropolis-Hastings algorithms using a prefetching approach
- Well-posed stochastic extensions of ill-posed linear problems
- Analysis of the Hessian for inverse scattering problems: I. Inverse shape scattering of acoustic waves
- Analysis of the Hessian for inverse scattering problems: II. Inverse medium scattering of acoustic waves
- Inverse problems: A Bayesian perspective
- A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
- A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems, Part II: Stochastic Newton MCMC with Application to Ice Sheet Flow Inverse Problems
- Randomize-Then-Optimize: A Method for Sampling from Posterior Distributions in Nonlinear Inverse Problems
- Numerical PDE-Constrained Optimization
- Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo
- Likelihood-informed dimension reduction for nonlinear inverse problems
- Computational Optimization of Systems Governed by Partial Differential Equations
- Optimization with PDE Constraints
- Lectures on Stochastic Programming
- Optimal Scaling of Discrete Approximations to Langevin Diffusions
- Variational Analysis
- Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods
- A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems
- Linear inverse problems for generalised random variables
- An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
- Equation of State Calculations by Fast Computing Machines
- A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion
- Introduction to Bayesian Scientific Computing
- Monte Carlo sampling methods using Markov chains and their applications
- MAP estimators and their consistency in Bayesian nonparametric inverse problems
- MCMC methods for functions: modifying old algorithms to make them faster
- Stochastic Equations in Infinite Dimensions
