Analysis and Applied Mathematics Seminar
Nathan Glatt-Holtz
Tulane University
A Bayesian approach to quantifying uncertainty in divergence free flows
Abstract: We treat a statistical regularization of the ill-posed inverse problem of estimating a divergence free flow field $u$
from the partial and noisy observation of a passive scalar $\theta$ which is advected by $u$. Our solution is a Bayesian
posterior distribution, that is a probability measure $\mu$ of the space of divergence free flow fields which
precisely quantifies uncertainties in $u$ once one specifies models for measurement error and a prior knowledge
for $u$. In this talk we survey some of our recent work which analyzes $\mu$ both analytically and numerically.
In particular we discuss a posterior contraction (consistency) result as well as some Markov Chain Monte Carlo
(MCMC) algorithms which we have developed, refined and rigorously analyzed to effectively sample from $\mu$.
This is joint work with Jeff Borggaard, Justin Krometis and Cecilia Mondaini.
Monday April 26, 2021 at 4:00 PM in Zoom