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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A nested particle filter for online Bayesian param
eter estimation in state-space systems - Miguez\,
J (Universidad Carlos III de Madrid)
DTSTART;TZID=Europe/London:20140430T113000
DTEND;TZID=Europe/London:20140430T123000
UID:TALK52345AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52345
DESCRIPTION:We address the problem of approximating the probab
ility measure of the fixed parameters of a state-s
pace dynamic system using a sequential Monte Carlo
method (SMC). The proposed approach relies on a n
ested structure that employs two layers of particl
e filters to approximate the posterior probability
law of the static parameters and the dynamic vari
ables of the system of interest\, in the vein of t
he recent SMC^2 algorithm. However\, different fro
m the SMC^2 scheme\, the proposed algorithm operat
es in a purely recursive manner and the scheme for
the rejuvenation of the particles in the paramete
r space is simpler. We show analytical results on
the approximation of integrals of real bounded fun
ctions with respect to the posterior distribution
of the system parameters computed via the proposed
scheme. For a finite time horizon and under mild
assumptions\, we prove that the approximation erro
rs vanish with the usual 1/?N rate\, where N is th
e number of particles in the parameter space. Unde
r a set of stronger assumptions related to (i) the
stability of the optimal filter for the model\, (
ii) the compactness of the parameter and state spa
ces and (iii) certain bounds on the family of like
lihood functions\, we prove that the convergence o
f the approximation errors is uniform over time\,
and provide an explicit rate function. The uniform
convergence result has some relevant consequences
. One of them is that the proposed scheme can asym
ptotically identify the parameter values for a cla
ss of state-space models. A subset of the assumpti
ons that yield uniform convergence also lead to a
positive lower bound\, uniform over time and the n
umber of particles\, on the normalized effective s
ample size the filter. We conclude with a simple n
umerical example that illustrates some of the theo
retical findings\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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