Bayesian Inverse Problems Are Usually Well-Posed

Bayesian Imaging Using Plug & Play Priors: When Langevin Meets Tweedie

(2022) Rémi Laumont et al.   SIAM Journal on Imaging Sciences

On Bayesian data assimilation for PDEs with ill-posed forward problems

(2022) S Lanthaler et al.   INVERSE PROBLEMS

Bayesian Imaging with Data-Driven Priors Encoded by Neural Networks

(2022) Matthew Holden et al.   SIAM Journal on Imaging Sciences

Bayesian approach for limited-aperture inverse acoustic scattering with total variation prior

(2022) Xiao-Mei Yang et al.   APPLICABLE ANALYSIS

Analysis of stochastic gradient descent in continuous time

(2021) Jonas Latz   STATISTICS AND COMPUTING

On the local Lipschitz stability of Bayesian inverse problems

(2020) Björn Sprungk   INVERSE PROBLEMS

Bridging the gap between constant step size stochastic gradient descent and Markov chains

(2020) Aymeric Dieuleveut et al.   ANNALS OF STATISTICS

Fast sampling of parameterised Gaussian random fields

(2019) Jonas Latz et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

An application of sparse measure valued Bayesian inversion to acoustic sound source identification

(2019) Sebastian Engel et al.   INVERSE PROBLEMS

On uniform continuity of posterior distributions

(2019) Emanuele Dolera et al.   STATISTICS & PROBABILITY LETTERS

Perturbation theory for Markov chains via Wasserstein distance

(2018) Daniel Rudolf et al.   BERNOULLI

Multilevel Sequential 2 Monte Carlo for Bayesian inverse problems

(2018) Jonas Latz et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Uncertainty Quantification in Graph-Based Classification of High Dimensional Data

(2018) Andrea L. Bertozzi et al.   SIAM-ASA Journal on Uncertainty Quantification

Equivalence of weak and strong modes of measures on topological vector spaces

(2018) Han Cheng Lie et al.   INVERSE PROBLEMS

Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion

(2018) Josef Dick et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors

(2017) T. J. Sullivan   Inverse Problems and Imaging

Posterior consistency for Gaussian process approximations of Bayesian posterior distributions

(2017) Andrew M. Stuart et al.   MATHEMATICS OF COMPUTATION

Well-Posed Bayesian Inverse Problems: Priors with Exponential Tails

(2017) Bamdad Hosseini et al.   SIAM-ASA Journal on Uncertainty Quantification

Well-Posed Bayesian Inverse Problems with Infinitely Divisible and Heavy-Tailed Prior Measures

(2017) Bamdad Hosseini   SIAM-ASA Journal on Uncertainty Quantification

A Bayesian level set method for geometric inverse problems

(2016) Marco Iglesias et al.   INTERFACES AND FREE BOUNDARIES

Selection, calibration, and validation of models of tumor growth

(2016) E. A. B. F. Lima et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Hierarchical Bayesian level set inversion

(2016) Matthew M. Dunlop et al.   STATISTICS AND COMPUTING

Maximuma posterioriprobability estimates in infinite-dimensional Bayesian inverse problems

(2015) T Helin et al.   INVERSE PROBLEMS

Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems

(2015) Oliver G. Ernst et al.   SIAM-ASA Journal on Uncertainty Quantification

Well-posed Bayesian geometric inverse problems arising in subsurface flow

(2014) Marco A Iglesias et al.   INVERSE PROBLEMS

MAP estimators and their consistency in Bayesian nonparametric inverse problems

(2013) M Dashti et al.   INVERSE PROBLEMS

Bayesian posterior contraction rates for linear severely ill-posed inverse problems

(2013) Sergios Agapiou et al.   Journal of Inverse and Ill-Posed Problems

Sparse deterministic approximation of Bayesian inverse problems

(2012) C Schwab et al.   INVERSE PROBLEMS

Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem

(2011) M. Dashti et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Inverse problems: A Bayesian perspective

(2010) A. M. Stuart   ACTA NUMERICA

A Stochastic Collocation Approach to Bayesian Inference in Inverse Problems

(2009) Youssef Marzouk et al.   Communications in Computational Physics

Stopping rules for a nonnegatively constrained iterative method for ill-posed Poisson imaging problems

(2008) Johnathan M. Bardsley   BIT NUMERICAL MATHEMATICS