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StochastikKolloquium
Bayesian Probabilistic Numerical Methods
21.11.2018, 11:15 - 12:15
Speaker:Prof. Dr. Tim Sullivan, Freie Universität Berlin/Zuse-Institut Berlin
Location:Institut für Informatik, Goldschmidtstrasse 7SR 5.101Gras Geo Map
Organizer:Institut für Mathematische Stochastik
Details:
Numerical computation --- such as numerical solution of a PDE --- can modelled as a statistical inverse problem in its own right. The popular Bayesian approach to inversion is considered, wherein a posterior distribution is induced over the object of interest by conditioning a prior distribution on the same finite information that would be used in a classical numerical method, thereby restricting attention to a meaningful subclass of probabilistic numerical methods distinct from classical average-case analysis and information-based complexity. The main technical consideration here is that the data are non-random and thus the standard Bayes' theorem does not hold. General conditions will be presented under which numerical methods based upon such Bayesian probabilistic foundations are well-posed, and a sequential Monte-Carlo method will be shown to provide consistent estimation of the posterior. The paradigm is extended to computational ''pipelines'', through which a distributional quantification of numerical error can be propagated. A sufficient condition is presented for when such propagation can be endowed with a globally coherent Bayesian interpretation, based on a novel class of probabilistic graphical models designed to represent a computational work-flow. The concepts are illustrated through explicit numerical experiments involving both linear and non-linear PDE models.
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Type:Colloquium
Language:English
Category:Research
Host:Dozenten des Instituts für Mathematische Stochastik
Contact:0551-39172100stochastik@uni-goettingen.de
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