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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Statistical Inference in Nonlinear Spaces via Maxi
mum Likelihood and Diffusion Bridge Simulation - S
tefan Sommer (Københavns Universitet (University o
f Copenhagen))
DTSTART;TZID=Europe/London:20171116T140000
DTEND;TZID=Europe/London:20171116T144500
UID:TALK95152AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/95152
DESCRIPTION:Co-authors: Darryl D. Holm (Imperial Colleg
e London)\, Alexis Arnaudon (Imperial College Lon
don) \, Sarang Joshi (University of Utah)
An alternative to performin
g statistical inference in manifolds by optimizati
ng least squares criterions such as those defining
the Frechet mean is to optimize the likelihood of
data. This approach emphasizes maximum likelihood
means over Frechet means\, and it in general allo
ws generalization of Euclidean statistical procedu
res defined via the data likelihood. While paramet
ric families of probability distributions are gene
rally hard to construct in nonlinear spaces\, tran
sition densities of stochastic processes provide a
geometrically natural way of defining data likeli
hoods. Examples of this includes the stochastic EP
Diff framework\, Riemannian Brownian motions and a
nisotropic generalizations of the Euclidean normal
distribution. In the talk\, we discuss likeliood
based inference on manifolds and procedures for ap
proximating data likelihood by simulation of manif
old and Lie group valued diffusion bridges.
Related Links
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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