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SUMMARY:Bayesian probabilistic numerical methods - Tim Sullivan (Freie Uni
 versität Berlin\; Konrad-Zuse-Zentrum für Informationstechnik Berlin)
DTSTART:20180410T140000Z
DTEND:20180410T150000Z
UID:TALK103597@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this work\, numerical computation - such as numerical solut
 ion of a PDE - is treated as a statistical inverse problem in its own righ
 t.  The popular Bayesian approach to inversion is considered\, wherein a p
 osterior distribution is induced over the object of interest by conditioni
 ng a prior distribution 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&#39\;
  theorem does not hold.  General conditions will be presented under which 
 such Bayesian probabilistic numerical methods are well-posed\, and a seque
 ntial Monte-Carlo method will be shown to provide consistent estimation of
  the posterior.  The paradigm is extended to computational ``pipelines&#39
 \;&#39\;\, through which a distributional quantification of numerical erro
 r 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 of probabilistic graphical models designed to rep
 resent a computational work-flow.  The concepts are illustrated through ex
 plicit numerical experiments involving both linear and non-linear PDE mode
 ls.  This is joint work with Jon Cockayne\, Chris Oates\, and Mark Girolam
 i.  Further details are available in the preprint arXiv:1702.03673.
LOCATION:Seminar Room 1\, Newton Institute
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