Bayesian Inverse Problems Are Usually Well-Posed
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Publication:6115454
DOI10.1137/23m1556435OpenAlexW4385663870MaRDI QIDQ6115454
Publication date: 10 August 2023
Published in: SIAM Review (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/23m1556435
total variationinverse problemswell-posednessKullback-Leibler divergenceBayesian inferenceWasserstein
Computational learning theory (68Q32) Bayesian inference (62F15) Sensitivity, stability, well-posedness (49K40) Learning and adaptive systems in artificial intelligence (68T05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)
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Cites Work
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- A Bayesian level set method for geometric inverse problems
- Multilevel sequential Monte Carlo for Bayesian inverse problems
- Stopping rules for a nonnegatively constrained iterative method for ill-posed Poisson imaging problems
- Hierarchical Bayesian level set inversion
- Perturbation theory for Markov chains via Wasserstein distance
- What is a statistical model? (With comments and rejoinder).
- Fast sampling of parameterised Gaussian random fields
- Mathematical image processing. Translated from the German
- Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors
- Bayesian posterior contraction rates for linear severely ill-posed inverse problems
- Analysis of stochastic gradient descent in continuous time
- Bridging the gap between constant step size stochastic gradient descent and Markov chains
- Stability of doubly-intractable distributions
- Higher order quasi-Monte Carlo integration for Bayesian PDE inversion
- On uniform continuity of posterior distributions
- High-dimensional Bayesian inference via the unadjusted Langevin algorithm
- No interpretation of probability
- Linear Inverse Problems
- Regularization Methods for Ill-Posed Problems
- Asymmetric Topologies on Statistical Manifolds
- Selection, calibration, and validation of models of tumor growth
- Sparse deterministic approximation of Bayesian inverse problems
- Inverse problems: A Bayesian perspective
- Well-posed Bayesian geometric inverse problems arising in subsurface flow
- Introduction to Uncertainty Quantification
- Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem
- Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications to Image Restoration
- Uncertainty Quantification in Graph-Based Classification of High Dimensional Data
- Maximuma posterioriprobability estimates in infinite-dimensional Bayesian inverse problems
- Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems
- Mathematical Foundations of Infinite-Dimensional Statistical Models
- A First Course in the Numerical Analysis of Differential Equations
- An Inverse Problem for the Steady State Diffusion Equation
- Probability Theory
- How Deep Are Deep Gaussian Processes?
- Posterior consistency for Gaussian process approximations of Bayesian posterior distributions
- Well-Posed Bayesian Inverse Problems with Infinitely Divisible and Heavy-Tailed Prior Measures
- LII. An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S
- Can one use total variation prior for edge-preserving Bayesian inversion?
- On Choosing and Bounding Probability Metrics
- On the Well-posedness of Bayesian Inverse Problems
- An application of sparse measure valued Bayesian inversion to acoustic sound source identification
- Erratum: Equivalence of weak and strong modes of measures on topological vector spaces (2018 Inverse Problems 34 115013)
- On the local Lipschitz stability of Bayesian inverse problems
- On Bayesian data assimilation for PDEs with ill-posed forward problems
- Bayesian Imaging Using Plug & Play Priors: When Langevin Meets Tweedie
- Bayesian Imaging with Data-Driven Priors Encoded by Neural Networks
- Bayesian Parameter Identification in Cahn--Hilliard Models for Biological Growth
- Bayesian Probabilistic Numerical Methods
- Well-Posed Bayesian Inverse Problems: Priors with Exponential Tails
- Principles of Statistical Inference
- MAP estimators and their consistency in Bayesian nonparametric inverse problems
- A Stochastic Approximation Method
- Probability, Frequency and Reasonable Expectation
- Optimal Transport