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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Amplitude and phase variation of point processes -
Victor Panaretos (EPFL - Ecole Polytechnique Fédé
rale de Lausanne)
DTSTART;TZID=Europe/London:20180529T110000
DTEND;TZID=Europe/London:20180529T120000
UID:TALK106417AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/106417
DESCRIPTION:The amplitude variation of a real random field X(t
) consists in its random oscillations in its range
space (the "y-axis")\, typically encapsulated by
its (co)variation around a mean level. In contrast
\, phase variation refers to fluctuations in its d
omain (the "x-axis")\, often caused by random time
changes or spatial deformations. We consider the
problem of identifiably formalising similar notion
s for (potentially spatial) point processes\, and
of nonparametrically separating them based on real
isations of i.i.d. copies of the phase-varying poi
nt process. The key element of our approach is the
use of the theory of optimal transportation of me
asure\, which is proven to be the natural formalis
m for the problem under the usual assumptions impo
sed. It is shown to allow the consistent separatio
n of the two types of variation for point processe
s over Euclidean domains\, under no parametric res
trictions\, including convergence rates\, and even
asymptotic distributions in some cases. \;(Ba
sed on joint work with Y. Zemel\, Gö\;ttingen.

LOCATION:Seminar Room 2\, Newton Institute
CONTACT:info@newton.ac.uk
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