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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Bayesian experimental design for percolation and o
ther random graph models - Bejan\, A (University o
f Cambridge)
DTSTART;TZID=Europe/London:20110720T170000
DTEND;TZID=Europe/London:20110720T173000
UID:TALK32107AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32107
DESCRIPTION:The problem of optimal arrangement of nodes of a r
andom graph will be discussed in this workshop. Th
e nodes of graphs under study are fixed\, but thei
r edges are random and established according to th
e so called edge-probability function. This functi
on may depend on the weights attributed to the pai
rs of graph nodes (or distances between them) and
a statistical parameter. It is the purpose of expe
rimentation to make inference on the statistical p
arameter and\, thus\, to learn about it as much as
possible. We also distinguish between two differe
nt experimentation scenarios: progressive and inst
ructive designs. We adopt a utility-based Bayesia
n framework to tackle this problem. We prove that
the infinitely growing or diminishing node config
urations asymptotically represent the worst node a
rrangements. We also obtain the exact solution to
the optimal design problem for proximity (geometri
c) graphs and numerical solution for graphs with t
hreshold edge-probability functions. We use simula
tion based optimisation methods\, mainly Monte Ca
rlo and Markov Chain Monte Carlo\, in order to obt
ain solution in the general case. We study the op
timal design problem for inference based on partia
l observations of random graphs by employing data
augmentation technique. In particular\, we conside
r inference and optimal design problems for finite
open clusters from bond percolation on the intege
r lattices and derive a range of both numerical an
d analytical results for these graphs. (Our motiva
tion here is that open clusters in bond percolatio
n may be seen as final outbreaks of an SIR epidemi
c with constant infectious times.) We introduce i
nner-outer design plots by considering a bounded r
egion of the lattice and deleting some of the lat
tice nodes within this region and show that the 'm
ostly populated' designs are not necessarily optim
al in the case of incomplete observations under bo
th progressive and instructive design scenarios. S
ome of the obtained results may generalise to othe
r lattices.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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