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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Bayesian probabilistic numerical methods - Tim Sul
livan (Freie Universität Berlin\; Konrad-Zuse-Zent
rum für Informationstechnik Berlin)
DTSTART;TZID=Europe/London:20180410T150000
DTEND;TZID=Europe/London:20180410T160000
UID:TALK103597AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/103597
DESCRIPTION:In this work\, numerical computation - such as num
erical solution of a PDE - is treated as a statist
ical inverse problem in its own right. The popula
r Bayesian approach to inversion is considered\, w
herein a posterior distribution is induced over th
e object of interest by conditioning a prior distr
ibution on the same finite information that would
be used in a classical numerical method. The main
technical consideration is that the data in this
context are non-random and thus the standard Bayes
'\; theorem does not hold. General conditions
will be presented under which such Bayesian probab
ilistic numerical methods are well-posed\, and a s
equential Monte-Carlo method will be shown to prov
ide consistent estimation of the posterior. The p
aradigm is extended to computational ``pipelines&#
39\;'\;\, through which a distributional quanti
fication of numerical error can be propagated. A
sufficient condition is presented for when such pr
opagation can be endowed with a globally coherent
Bayesian interpretation\, based on a novel class o
f probabilistic graphical models designed to repre
sent a computational work-flow. The concepts are
illustrated through explicit numerical experiments
involving both linear and non-linear PDE models.
This is joint work with Jon Cockayne\, Chris Oate
s\, and Mark Girolami. Further details are availa
ble in the preprint arXiv:1702.03673.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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