Masoumeh Dashti, Andrew M. Stuart
Published 2013-02-27, updated 2014-12-19Version 3
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.
Comments: Preliminary version of lecture notes to appear in Handbook of Uncertainty Quantification, Editors R. Ghanem, D. Higdon and H. Owhadi, Springer, 2016. arXiv admin note: text overlap with arXiv:0907.4178 by other authors
Absolutely continuous copulas with prescribed support constructed by differential equations, with an application in toxicology
Convergence of Probability Densities using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification: Extensions to $L^p$
Inverse Problems for Ergodicity of Markov Chains
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