Open Collections

High-dimensional Bayesian inference and convex geometry: theory, methods, and algorithms

Banff International Research Station for Mathematical Innovation and Discovery

This presentation 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, 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.

Mathematics; Statistics; Statistical mechanics, structure of matter; Statistical mechanics

video/mp4

Author affiliation: Heriot Watt University

2019-05-14

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/70150

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/