Priorconditioned CGLS-Based Quasi-MAP Estimate, Statistical Stopping Rule, and Ranking of Priors

DOI10.1137/16M108272XzbMath1392.65046OpenAlexW2767142010MaRDI QIDQ5372638

Francesca Pitolli, J. Prezioso, Barbara Vantaggi, Erkki Somersalo, Daniela Calvetti

Publication date: 27 October 2017

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

Full work available at URL: https://doi.org/10.1137/16m108272x

zbMATH Keywords

regularizationinverse problemsiterative methodsKrylov subspace

Mathematics Subject Classification ID

Bayesian inference (62F15) Iterative numerical methods for linear systems (65F10) Inverse problems in optimal control (49N45) Preconditioners for iterative methods (65F08)

Related Items (5)

Inducing sparsity via the horseshoe prior in imaging problems ⋮ Sparsity Promoting Hybrid Solvers for Hierarchical Bayesian Inverse Problems ⋮ Bayes Meets Krylov: Statistically Inspired Preconditioners for CGLS ⋮ Sparse reconstructions from few noisy data: analysis of hierarchical Bayesian models with generalized gamma hyperpriors ⋮ Overcomplete representation in a hierarchical Bayesian framework

Uses Software

• LSQR
• Regularization tools
• UTV
• CRAIG

Cites Work

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• Analysis of the Gibbs Sampler for Hierarchical Inverse Problems
• Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation
• Hypermodels in the Bayesian imaging framework
• A priori weighting for parameter estimation
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Bayes Meets Krylov: Statistically Inspired Preconditioners for CGLS
• Iterative Krylov Methods for Large Linear Systems
• Oblique projections and standard‐form transformations for discrete inverse problems
• Introduction to Bayesian Scientific Computing
• Priorconditioners for linear systems
• Methods of conjugate gradients for solving linear systems

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