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SUMMARY:Bayesian Probabilistic Numerical Methods - Chris Oates - Newcastle
  Universtity
DTSTART:20171129T140000Z
DTEND:20171129T150000Z
UID:TALK80341@talks.cam.ac.uk
CONTACT:Rachel Furner
DESCRIPTION:In this talk\, numerical computation - such as numerical solut
 ion of a PDE – will be treated as an inverse problem in its own right. T
 he popular Bayesian approach to inversion is considered\, wherein a poster
 ior 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. The main technical consideration is that the d
 ata in this context are non-random and thus the standard Bayes' theorem do
 es not hold. General conditions will be presented under which such Bayesia
 n probabilistic numerical methods are well-posed\, and a sequential Monte-
 Carlo method will be shown to provide consistent estimation of the posteri
 or. The paradigm will then be extended to computational ``pipelines''\, th
 rough which a distributional quantification of numerical error can be prop
 agated. A sufficient condition can be obtained for when such propagation c
 an be endowed with a globally coherent Bayesian interpretation\, based on 
 a novel class of probabilistic graphical models designed to represent a co
 mputational work-flow. The concepts are illustrated through explicit numer
 ical experiments involving both linear and non-linear PDE models. Full det
 ails are available in arXiv:1702.03673.
LOCATION:MR5 Centre for Mathematical Sciences
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