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SUMMARY:Analysis of an interacting particle scheme for rare event estimati
 on - Cai\, Y\, Dupuis\, P (Brown)
DTSTART:20100622T080000Z
DTEND:20100622T085000Z
UID:TALK25316@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A number of schemes for Monte Carlo estimation of rare events 
 are based on splitting particles when they reach certain thresholds. Among
  these is the interacting particle scheme introduced in [1] and also discu
 ssed at recent RESIM conferences. A feature of this approach that is consi
 dered attractive is that the total number of particles (and hence the tota
 l computational effort needed to generate a sample) is controlled. Althoug
 h this scheme has been observed to perform well as the probability being e
 stimated gets small\, prior analysis has tended to focus on limits where t
 he number of particles gets large with the probability held fixed. One rea
 son is that all particles are statistically re-coupled at each threshold\,
  and hence limits where the number of particles is fixed and the probabili
 ty gets small are difficult to analyze. We introduce some new techniques f
 or the large deviation analysis of such systems. Although the large deviat
 ion scaling for the probability of interest is what is known as a small no
 ise large deviation limit\, the analysis of interacting particles systems 
 requires ideas from the large deviation theory for occupation measures of 
 Markov chains. [1] P. Del Moral and J. Garnier. Genealogical particle anal
 ysis of rare events. Ann. Appl. Probab.\, 15:24962534\, 2005.
LOCATION:Seminar Room 1\, Newton Institute
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