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arxiv: 1302.6989 · v4 · pith:3EJXJ75Lnew · submitted 2013-02-27 · 🧮 math.PR

The Bayesian Approach To Inverse Problems

Masoumeh Dashti , Andrew M. Stuart This is my paper
classification 🧮 math.PR
keywords approachbayesianinversemathematicalproblemsalgorithmsapplicationsblending
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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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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Frequentist Coverage of Bayes Posteriors in Nonlinear Inverse Problems with Gaussian Priors

    math.ST 2024-07 unverdicted novelty 7.0

    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.