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John Bardsley
Sampling Methods for Uncertainty Quantification in Inverse Problems

Abstract: Many solution methods for inverse problems compute the maximum a posteriori (MAP) estimator, or equivalently, the regularized solution, by solving an optimization problem. Uncertainty quantification (UQ), on the other hand, typically requires sampling from the Bayesian posterior density function. In this talk, we bring these two ideas together and present posterior sampling methods that make use of existing numerical methods for computing regularized solutions/MAP estimators. Theoretically correct sampling methods for both linear and nonlinear inverse problems will be presented.