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

Presented by: 
Marcelo Pereyra Heriot-Watt University
Date: 
Thursday 2nd November 2017 - 14:50 to 15:40
Venue: 
INI Seminar Room 1
Abstract: 
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons