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CATEGORIES:CCIMI Seminars
SUMMARY:Bayesian Probabilistic Numerical Methods - Chris O
ates - Newcastle Universtity
DTSTART;TZID=Europe/London:20171129T140000
DTEND;TZID=Europe/London:20171129T150000
UID:TALK80341AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/80341
DESCRIPTION:In this talk\, numerical computation - such as num
erical solution of a PDE – will be treated as an i
nverse problem in its own right. The popular Bayes
ian approach to inversion is considered\, wherein
a posterior distribution is induced over the objec
t of interest by conditioning a prior distribution
on the same finite information that would be used
in a classical numerical method. The main technic
al consideration is that the data in this context
are non-random and thus the standard Bayes' theore
m does not hold. General conditions will be presen
ted under which such Bayesian probabilistic numeri
cal methods are well-posed\, and a sequential Mont
e-Carlo method will be shown to provide consistent
estimation of the posterior. The paradigm will th
en be extended to computational ``pipelines''\, th
rough which a distributional quantification of num
erical error can be propagated. A sufficient condi
tion can be obtained for when such propagation can
be endowed with a globally coherent Bayesian inte
rpretation\, based on a novel class of probabilist
ic graphical models designed to represent a comput
ational work-flow. The concepts are illustrated th
rough explicit numerical experiments involving bot
h linear and non-linear PDE models. Full details a
re available in arXiv:1702.03673.
LOCATION:MR5 Centre for Mathematical Sciences
CONTACT:Rachel Furner
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