Bayesian Inverse Problems with $l_1$ Priors: A Randomize-Then-Optimize Approach
From MaRDI portal
Publication:5372623
DOI10.1137/16M1080938zbMath1422.65028arXiv1607.01904OpenAlexW2503750833MaRDI QIDQ5372623
Zheng Wang, Youssef M. Marzouk, Tiangang Cui, Antti Solonen, Johnathan M. Bardsley
Publication date: 27 October 2017
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1607.01904
Bayesian inference (62F15) Monte Carlo methods (65C05) Numerical solution to inverse problems in abstract spaces (65J22)
Related Items
A blocking scheme for dimension-robust Gibbs sampling in large-scale image deblurring ⋮ Learning physics-based models from data: perspectives from inverse problems and model reduction ⋮ Prior normalization for certified likelihood-informed subspace detection of Bayesian inverse problems ⋮ Sparse Online Variational Bayesian Regression ⋮ An Acceleration Strategy for Randomize-Then-Optimize Sampling Via Deep Neural Networks ⋮ Bayesian approach for limited-aperture inverse acoustic scattering with total variation prior ⋮ Sparse Bayesian inference with regularized Gaussian distributions * ⋮ Scalable Optimization-Based Sampling on Function Space ⋮ Besov-Laplace priors in density estimation: optimal posterior contraction rates and adaptation ⋮ Wavelet-based priors accelerate maximum-a-posteriori optimization in Bayesian inverse problems ⋮ Optimization-Based Markov Chain Monte Carlo Methods for Nonlinear Hierarchical Statistical Inverse Problems ⋮ $l_p$ Regularization for Ensemble Kalman Inversion ⋮ An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems ⋮ Efficient Bayesian Computation by Proximal Markov Chain Monte Carlo: When Langevin Meets Moreau ⋮ Implicit sampling for hierarchical Bayesian inversion and applications in fractional multiscale diffusion models ⋮ Two Metropolis--Hastings Algorithms for Posterior Measures with Non-Gaussian Priors in Infinite Dimensions ⋮ Edge-Promoting Adaptive Bayesian Experimental Design for X-ray Imaging
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Variable transformation to obtain geometric ergodicity in the random-walk Metropolis algorithm
- Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
- Nonlinear total variation based noise removal algorithms
- The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
- A random map implementation of implicit filters
- Diffusion limits of the random walk Metropolis algorithm in high dimensions
- Besov priors for Bayesian inverse problems
- Implicit particle filters for data assimilation
- Bayesian inference with optimal maps
- Monte Carlo errors with less errors
- Exponential convergence of Langevin distributions and their discrete approximations
- Weak convergence and optimal scaling of random walk Metropolis algorithms
- Statistical and computational inverse problems.
- Rates of convergence of the Hastings and Metropolis algorithms
- Discretization-invariant Bayesian inversion and Besov space priors
- Dimension-independent likelihood-informed MCMC
- An adaptive version for the Metropolis adjusted Langevin algorithm with a truncated drift
- Monte Carlo strategies in scientific computing.
- Inverse problems: A Bayesian perspective
- A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
- Transport Map Accelerated Markov Chain Monte Carlo
- Sparsity-promoting Bayesian inversion
- Sampling-Based Approaches to Calculating Marginal Densities
- Ten Lectures on Wavelets
- Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography
- Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods
- Linear and Nonlinear Inverse Problems with Practical Applications
- An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
- Can one use total variation prior for edge-preserving Bayesian inversion?
- Inverse Problem Theory and Methods for Model Parameter Estimation
- Computational Methods for Inverse Problems
- Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors
- Equation of State Calculations by Fast Computing Machines
- Introduction to Bayesian Scientific Computing
- Monte Carlo sampling methods using Markov chains and their applications
- Laplace-distributed increments, the Laplace prior, and edge-preserving regularization
- An adaptive Metropolis algorithm
- MCMC methods for functions: modifying old algorithms to make them faster
This page was built for publication: Bayesian Inverse Problems with $l_1$ Priors: A Randomize-Then-Optimize Approach
