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SUMMARY:Least-action filtering - Rogers\, C (Cambridge)
DTSTART:20100615T085000Z
DTEND:20100615T094000Z
UID:TALK25292@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:This talk studies the filtering of a partially-observed multid
 imensional diffusion process using the principle of least action\, equival
 ently\, maximum-likelihood estimation. We show how the most likely path of
  the unobserved part of the diffusion can be determined by solving a shoot
 ing ODE\, and then we go on to study the (approximate) conditional distrib
 ution of the diffusion around the most likely path\; this turns out to be 
 a zero-mean Gaussian process which solves a linear SDE whose time-dependen
 t coefficients can be identified by solving a first-order ODE with an init
 ial condition. This calculation of the conditional distribution can be use
 d as a way to guide SMC methods to search relevant parts of the state spac
 e\, which may be valuable in high-dimensional problems\, where SMC struggl
 es\; in contrast\, ODE solution methods continue to work well even in mode
 rately large dimension.
LOCATION:Seminar Room 1\, Newton Institute
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