Abstract
Abstract
This article shows that a large class of posterior measures that are absolutely continuous with respect to a Gaussian prior have strong maximum a posteriori estimators in the sense of Dashti et al (2013 Inverse Problems
29 095017). This result holds in any separable Banach space and applies in particular to nonparametric Bayesian inverse problems with additive noise. When applied to Bayesian inverse problems, this significantly extends existing results on maximum a posteriori estimators by relaxing the conditions on the log-likelihood and on the space in which the inverse problem is set.
Funder
University of Warwick
Engineering and Physical Sciences Research Council
Subject
Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science