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SUMMARY:The Bayesian Approach To Inverse Problems - Andrew Stuart\, Univer
 sity of Warwick
DTSTART:20130308T160000Z
DTEND:20130308T170000Z
UID:TALK43907@talks.cam.ac.uk
CONTACT:24390
DESCRIPTION:Many problems in the physical sciences require the determinati
 on of an unknown field from a finite set of indirect measurements. Example
 s include oceanography\, oil recovery\, water resource management and weat
 her forecasting. The Bayesian approach to these problems is natural for ma
 ny reasons\, including the under-determined and ill-posed nature of the in
 version\, the noise in the data and the uncertainty in the differential eq
 uation models used to describe complex mutiscale physics.\n\nIn this talk 
 I will describe the advantages of formulating Bayesian inversion on functi
 on space in order to solve these problems. I will overview theoretical res
 ults concerning well-posedness of the posterior distribution\, approximati
 on theorems for the posterior distribution\, and specially constructed MCM
 C methods to explore the posterior distribution when the prior is a Gaussi
 an random field. I will also highlight the widespread use by practitioners
  of various ad hoc algorithms such as the Ensemble Kalman Filter\, and the
  need for mathematical and statistical analysis of these ad hoc algorithms
 .\n\nIntroductory reading and references may be found in:\n\nhttp://arxiv.
 org/abs/1202.0709 [arxiv.org] http://arxiv.org/abs/1209.2736 [arxiv.org]
LOCATION:CMS\, MR12
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