MAP estimators for nonparametric Bayesian inverse problems in Banach spaces
Abstract
In order to rigorously define maximum-a-posteriori estimators for nonparametric Bayesian inverse problems for general Banach space valued parameters, we derive and prove certain previously postulated but unproven bounds on small ball probabilities. This allows us to prove existence of MAP estimators in the Banach space setting under very mild assumptions on the loglikelihood. As a similar statement so far (as far as the author is aware) only existed in the Hilbert space setting, this closes an important gap in the literature.
Keywords
Cite
@article{arxiv.2007.12760,
title = {MAP estimators for nonparametric Bayesian inverse problems in Banach spaces},
author = {Philipp Wacker},
journal= {arXiv preprint arXiv:2007.12760},
year = {2022}
}
Comments
This preprint contained incomplete ideas and even some errors. These gaps and mistakes have been closed by a recent preprint: arXiv:2207.00640 Due to the fact that the techniques and the scope have changed as well as the author list, I would like to withdraw this preprint