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SUMMARY:Amplitude and phase variation of point processes - Victor Panareto
 s (EPFL - Ecole Polytechnique Fédérale de Lausanne)
DTSTART:20180529T100000Z
DTEND:20180529T110000Z
UID:TALK106417@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The amplitude variation of a real random field X(t) consists i
 n its random oscillations in its range space (the "y-axis")\, typically en
 capsulated by its (co)variation around a mean level. In contrast\, phase v
 ariation refers to fluctuations in its domain (the "x-axis")\, often cause
 d by random time changes or spatial deformations. We consider the problem 
 of identifiably formalising similar notions for (potentially spatial) poin
 t processes\, and of nonparametrically separating them based on realisatio
 ns of i.i.d. copies of the phase-varying point process. The key element of
  our approach is the use of the theory of optimal transportation of measur
 e\, which is proven to be the natural formalism for the problem under the 
 usual assumptions imposed. It is shown to allow the consistent separation 
 of the two types of variation for point processes over Euclidean domains\,
  under no parametric restrictions\, including convergence rates\, and even
  asymptotic distributions in some cases.&nbsp\;(Based on joint work with Y
 . Zemel\, G&ouml\;ttingen.  <br><br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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