Wednesday, May 26, 2021 - 14:30 in ZOOM - Video Conference
A Bayesian Approach to Quantifying Uncertainty in Divergence Free Flows
A talk in the Bielefeld Stochastic Afternoon series by
Nathan Glatt-Holtz from Tulane University
| 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 θ which is advected by u. Our solution is a Bayesian posterior distribution, that is a probability measure μ 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 μ 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 μ. This is joint work with Jeff Borggaard, Justin Krometis and Cecilia Mondaini.
Please contact stochana@math.uni-bielefeld.de for Meeting-ID and Password.
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