Appears in collection : Statistical Modeling for Shapes and Imaging

This talk summarises some new developments in theory, methods, and algorithms for performing Bayesian inference in high-dimensional models that are log-concave, with application to mathematical and computational imaging in convex settings. These include new efficient stochastic simulation and optimisation Bayesian computation methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection; and methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; all illustrated with a range of mathematical imaging experiments.