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SUMMARY:Large clusters as rare events\, their simulation and connection to
  critical percolation - Andrei Bejan\, Computer Laboratory.
DTSTART:20090527T150000Z
DTEND:20090527T160000Z
UID:TALK18343@talks.cam.ac.uk
CONTACT:Sarah Lilienthal
DESCRIPTION:Inference and optimal design problems for finite clusters from
 \npercolation on the integer lattice Z^d^ or\, equivalently\,\nfor SIR epi
 demics evolving on a bounded subset of Z^d^\nwith constant life times are 
 considered. The corresponding\npercolation probability p is considered to 
 be unknown\, possibly\ndepending\, through the experimental design\, on ot
 her parameters. We\nconsider inference under each of the following two sce
 narios:\n\n(i) The observations consist of the set of sites which are ever
 \ninfected\, so that the routes by which infections travel are not\nobserv
 ed (in terms of the bond percolation process\, this corresponds\nto a know
 ledge of the connected component containing the initially\ninfected site--
 -the location of this site within the component not\nbeing relevant to inf
 erence for p).\n\n(ii) All that is observed is the _size_ of the set of si
 tes\nwhich are ever infected.\n\nWe discuss practical aspects of Bayesian 
 utility-based optimal\ndesigns for the former scenario and prove that the 
 sequence of MLE's\nfor p converges to the critical percolation probability
  p_c\nunder the latter scenario (when the size of the finite cluster\ngrow
 s).\n\nThis is a joint work with Professor Gavin Gibson and Dr Stan\nZacha
 ry\, both with Heriot-Watt University\, Edinburgh.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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