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SUMMARY:Statistical Inference in Nonlinear Spaces via Maximum Likelihood a
 nd Diffusion Bridge Simulation - Stefan Sommer (Københavns Universitet (U
 niversity of Copenhagen))
DTSTART:20171116T140000Z
DTEND:20171116T144500Z
UID:TALK95152@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Darryl D. Holm		(Imperial College London)\, 
 Alexis Arnaudon		(Imperial College London)        \, Sarang Joshi		(Univer
 sity of Utah)        <br></span><br> An alternative to performing statisti
 cal inference in manifolds by optimizating least squares criterions such a
 s those defining the Frechet mean is to optimize the likelihood of data. T
 his approach emphasizes maximum likelihood means over Frechet means\, and 
 it in general allows generalization of Euclidean statistical procedures de
 fined via the data likelihood. While parametric families of probability di
 stributions are generally hard to construct in nonlinear spaces\, transiti
 on densities of stochastic processes provide a geometrically natural way o
 f defining data likelihoods. Examples of this includes the stochastic EPDi
 ff framework\, Riemannian Brownian motions and anisotropic generalizations
  of the Euclidean normal distribution. In the talk\, we discuss likeliood 
 based inference on manifolds and procedures for approximating data likelih
 ood by simulation of manifold and Lie group valued diffusion bridges. <br>
 <br>Related Links<ul><li><a target="_blank" rel="nofollow" href="http://ww
 w-old.newton.ac.uk/cgi/https%3A%2F%2Farxiv.org%2Fabs%2F1703.09971">https:/
 /arxiv.org/abs/1703.09971</a></li><li><a target="_blank" rel="nofollow" hr
 ef="http://www-old.newton.ac.uk/cgi/https%3A%2F%2Farxiv.org%2Fabs%2F1612.0
 5323">https://arxiv.org/abs/1612.05323</a></li></ul>
LOCATION:Seminar Room 1\, Newton Institute
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