The paper establishes conservative frequentist coverage for Bayes credible intervals in nonlinear inverse problems with Gaussian priors under specified conditions, illustrated via an elliptic Darcy flow problem.
The Bayesian Approach To Inverse Problems
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abstract
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental in the quantification of uncertainty within applications involving the blending of mathematical models with data.
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EPEN jointly reconstructs diffusion-weighted images and estimates slab profiles from undersampled 3D multi-slab k-space using a bilinear model, CNN deep energy prior, and alternating minimization to suppress artifacts.
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Frequentist Coverage of Bayes Posteriors in Nonlinear Inverse Problems with Gaussian Priors
The paper establishes conservative frequentist coverage for Bayes credible intervals in nonlinear inverse problems with Gaussian priors under specified conditions, illustrated via an elliptic Darcy flow problem.