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CATEGORIES:Cambridge Centre for Analysis talks
SUMMARY:The Bayesian Approach to Inverse Problems - Profes
sor Andrew Stuart\, University of Warwick Mathemat
ics Institute
DTSTART;TZID=Europe/London:20140423T140000
DTEND;TZID=Europe/London:20140423T180000
UID:TALK51986AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/51986
DESCRIPTION:Probabilistic thinking is of growing importance in
many areas of mathematics. This short course will
demonstrate the beautiful mathematical framework\
,\ncoupled with practical algorithms\, which resul
ts from thinking probabilistically about inverse p
roblems arising in partial differential equations.
\n\nMany inverse problems in the physical sciences
require the determination of an unknown field fro
m a finite set of indirect measurements. Examples
include oceanography\, oil recovery\, water resour
ce management and weather forecasting. In the Baye
sian approach to these problems\, the unknown and
the data are modelled as a jointly varying random
variable\, and the solution of the inverse problem
is the distribution of the un- known given the da
ta.\n\nThis approach provides a natural way to pro
vide estimates of the unknown field\, together wit
h a quantification of the uncertainty associated w
ith\nthe estimate. It is hence a useful practical
modelling tool. However it also provides a very el
egant mathematical framework for inverse problems:
\nwhilst the classical approach to inverse problem
s leads to ill-posedness\, the Bayesian approach l
eads to a natural well-posedness and stability the
ory. Furthermore this framework provides a way of
deriving and developing algorithms which are well
suited to the formidable computational challenges
which arise from the conjunction of approximations
arising from the numerical analysis of partial di
fferential equations\, together with approximation
s of central limit theorem type arising from sampl
ing of measures.\n\nThe tools in mathematical anal
ysis which you will be exposed to during the cours
e lie at the intersection of probability and analy
sis\, and include Gaussian measures on Hilbert spa
ce\, metrics on probability\nmeasures\, conditiona
l probability and regularity estimates for ellipti
c PDEs and for the Navier-Stokes equation.
LOCATION:MR5
CONTACT:CCA
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