Bayesian Inverse Problems
Posterior sampling for ill-posed problems with Gaussian priors.
Bayesian Inverse Problems. Posterior sampling for ill-posed problems with Gaussian priors.
Foundations and canonical references
The standard treatments of bayesian inverse problems approach the subject from complementary angles. Kaipio, Statistical and Computational Inverse Problems (2005) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Recent technical contributions
A handful of recent papers carry the methodological frontier of bayesian inverse problems forward. Inverse problems: A Bayesian perspective (Stuart, 2010) is a primary reference for this area and develops new techniques or results that downstream work builds on.
Open methodological questions for bayesian inverse problems include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
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- textbook · primary · 2005Statistical and Computational Inverse Problemskaipio-2005, somersalo-2005
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