Fundamentals of statistical exponential families: with applications in statistical decision theory
Fundamentals of statistical exponential families: with applications in statistical decision theory
Existence and uniqueness for electrode models for electric current computed tomography
SIAM Journal on Applied Mathematics
An Introduction to Variational Methods for Graphical Models
Machine Learning
Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models
SIAM Journal on Scientific Computing
Expectation Consistent Approximate Inference
The Journal of Machine Learning Research
Stochastic spectral methods for efficient Bayesian solution of inverse problems
Journal of Computational Physics
Bayesian Inference and Optimal Design for the Sparse Linear Model
The Journal of Machine Learning Research
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
A variational Bayesian method to inverse problems with impulsive noise
Journal of Computational Physics
Expectation propagation for approximate Bayesian inference
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
SIAM Journal on Scientific Computing
Sparsity reconstruction in electrical impedance tomography: An experimental evaluation
Journal of Computational and Applied Mathematics
IEEE Transactions on Signal Processing
Bayesian inference with optimal maps
Journal of Computational Physics
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In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of efficiently delivering reliable estimates of the posterior mean and covariance, thereby providing an inverse solution together with quantified uncertainties. Some theoretical properties of the iterative algorithm are discussed, and the efficient implementation for an important class of problems of projection type is described. The method is illustrated with one typical nonlinear inverse problem, electrical impedance tomography with complete electrode model, under sparsity constraints. Numerical results for real experimental data are presented, and compared with that by Markov chain Monte Carlo. The results indicate that the method is accurate and computationally very efficient.