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SUMMARY:A nested particle filter for online Bayesian parameter estimation 
 in state-space systems - Miguez\, J (Universidad Carlos III de Madrid)
DTSTART:20140430T103000Z
DTEND:20140430T113000Z
UID:TALK52345@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We address the problem of approximating the probability measur
 e of the fixed parameters of a state-space dynamic system using a sequenti
 al Monte Carlo method (SMC). The proposed approach relies on a nested stru
 cture that employs two layers of particle filters to approximate the poste
 rior probability law of the static parameters and the dynamic variables of
  the system of interest\, in the vein of the recent SMC^2 algorithm. Howev
 er\, different from the SMC^2 scheme\, the proposed algorithm operates in 
 a purely recursive manner and the scheme for the rejuvenation of the parti
 cles in the parameter space is simpler. We show analytical results on the 
 approximation of integrals of real bounded functions with respect to the p
 osterior distribution of the system parameters computed via the proposed s
 cheme. For a finite time horizon and under mild assumptions\, we prove tha
 t the approximation errors vanish with the usual 1/?N rate\, where N is th
 e number of particles in the parameter space. Under a set of stronger assu
 mptions related to (i) the stability of the optimal filter for the model\,
  (ii) the compactness of the parameter and state spaces and (iii) certain 
 bounds on the family of likelihood functions\, we prove that the convergen
 ce of the approximation errors is uniform over time\, and provide an expli
 cit rate function. The uniform convergence result has some relevant conseq
 uences. One of them is that the proposed scheme can asymptotically identif
 y the parameter values for a class of state-space models. A subset of the 
 assumptions that yield uniform convergence also lead to a positive lower b
 ound\, uniform over time and the number of particles\, on the normalized e
 ffective sample size the filter. We conclude with a simple numerical examp
 le that illustrates some of the theoretical findings\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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