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Bayesian analysis and computation for convex inverse problems: theory, methods, and algorithms

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VMVW02 - Generative models, parameter learning and sparsity

This talk presents some new developments in theory, methods, and algorithms for performing Bayesian inference in high-dimensional inverse problems that are convex, with application to mathematical and computational imaging. These include new efficient stochastic simulation and optimisation Bayesian computation methods that tightly combine proximal optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The new theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments.

This talk is part of the Isaac Newton Institute Seminar Series series.

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