Well-Posed Bayesian Inverse Problems: Priors with Exponential Tails
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Publication:5269871
DOI10.1137/16M1076824zbMath1371.35349arXiv1604.02575WikidataQ115525637 ScholiaQ115525637MaRDI QIDQ5269871
Publication date: 28 June 2017
Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.02575
Parametric inference (62F99) Inverse problems for PDEs (35R30) Theoretical approximation in context of PDEs (35A35) Probability theory on linear topological spaces (60B11)
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Cites Work
- Unnamed Item
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- A mathematical introduction to compressive sensing
- Besov priors for Bayesian inverse problems
- A basis theory primer.
- Partial differential equations. I: Basic theory
- On the consistency of Bayes estimates
- Convex measures on locally convex spaces
- An introduction to partial differential equations
- Statistical and computational inverse problems.
- Discretization-invariant Bayesian inversion and Besov space priors
- Log-concave probability and its applications
- Inverse problems: A Bayesian perspective
- Well-posed Bayesian geometric inverse problems arising in subsurface flow
- Maximuma posterioriestimates in linear inverse problems with log-concave priors are proper Bayes estimators
- Analysis of the Gibbs Sampler for Hierarchical Inverse Problems
- Approximation of Bayesian Inverse Problems for PDEs
- Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem
- Sparsity-promoting Bayesian inversion
- Deblurring Images
- Maximuma posterioriprobability estimates in infinite-dimensional Bayesian inverse problems
- Hierarchical regularization for edge-preserving reconstruction of PET images
- The horseshoe estimator for sparse signals
- Foundations of Modern Probability
- Posterior consistency for Gaussian process approximations of Bayesian posterior distributions
- Computational Methods for Inverse Problems
- Introduction to Bayesian Scientific Computing
- On the Asymptotic Behavior of Bayes' Estimates in the Discrete Case
- MCMC methods for functions: modifying old algorithms to make them faster