Horseshoe Priors for Edge-Preserving Linear Bayesian Inversion

DOI10.1137/22m1510364arXiv2207.09147OpenAlexW4380085840MaRDI QIDQ6156655

Yiqiu Dong, Felipe Uribe, Per Christian Hansen

Publication date: 14 June 2023

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.09147

zbMATH Keywords

Gibbs samplerBayesian inverse problemsBayesian hierarchical modelinghorseshoe prioredge-preserving estimation

Mathematics Subject Classification ID

Bayesian inference (62F15) Ill-posedness and regularization problems in numerical linear algebra (65F22) Monte Carlo methods (65C05) Numerical methods for inverse problems for integral equations (65R32)

Related Items

Sparse Bayesian inference with regularized Gaussian distributions ^*, Inducing sparsity via the horseshoe prior in imaging problems

Cites Work

• Sparsity information and regularization in the horseshoe and other shrinkage priors
• Besov priors for Bayesian inverse problems
• The horseshoe estimator: posterior concentration around nearly black vectors
• Bayesian inference with optimal maps
• Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms
• Hierarchical Bayesian level set inversion
• Statistical and computational inverse problems.
• Markov chains for exploring posterior distributions. (With discussion)
• Cauchy Markov random field priors for Bayesian inversion
• Geometric ergodicity of Gibbs samplers for the horseshoe and its regularized variants
• On the convergence of the Laplace approximation and noise-level-robustness of Laplace-based Monte Carlo methods for Bayesian inverse problems
• Discretization-invariant Bayesian inversion and Besov space priors
• Shrinkage priors for Bayesian penalized regression
• AIR tools II: algebraic iterative reconstruction methods, improved implementation
• Mean field variational Bayes for elaborate distributions
• The Bayesian elastic net
• Bayesian neural network priors for edge-preserving inversion
• Preconditioned Krylov Subspace Methods for Sampling Multivariate Gaussian Distributions
• A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
• Deblurring Images
• The horseshoe estimator for sparse signals
• From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
• The Bayesian Lasso
• Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
• 10.1162/15324430152748236
• Hierachical Bayesian models and sparsity: ℓ ₂ -magic
• Well-Posed Bayesian Inverse Problems with Infinitely Divisible and Heavy-Tailed Prior Measures
• Bayes Meets Krylov: Statistically Inspired Preconditioners for CGLS
• Can one use total variation prior for edge-preserving Bayesian inversion?
• Gaussian Markov Random Fields
• High-Dimensional Gaussian Sampling: A Review and a Unifying Approach Based on a Stochastic Proximal Point Algorithm
• Computed Tomography: Algorithms, Insight, and Just Enough Theory
• A Hybrid Gibbs Sampler for Edge-Preserving Tomographic Reconstruction with Uncertain View Angles
• Sparsity Promoting Hybrid Solvers for Hierarchical Bayesian Inverse Problems
• Discrete Inverse Problems
• An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems
• Laplace-distributed increments, the Laplace prior, and edge-preserving regularization
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