BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Bayesian experimental design for percolation and other random grap
 h models - Bejan\, A (University of Cambridge)
DTSTART:20110720T160000Z
DTEND:20110720T163000Z
UID:TALK32107@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The problem of optimal arrangement of nodes of a random graph 
 will be discussed in this workshop. The nodes of graphs under study are fi
 xed\, but their edges are random and established according to the so calle
 d edge-probability function. This function may depend on the weights attri
 buted to the pairs of graph nodes (or distances between them) and a statis
 tical parameter. It is the purpose of experimentation to make inference on
  the statistical parameter and\, thus\, to learn about it as much as possi
 ble. We also distinguish between two different experimentation scenarios: 
 progressive and instructive designs.  We adopt a utility-based Bayesian fr
 amework to tackle this problem.  We prove that the infinitely growing or d
 iminishing node configurations asymptotically represent the worst node arr
 angements. We also obtain the exact solution to the optimal design problem
  for proximity (geometric) graphs and numerical solution for graphs with t
 hreshold edge-probability functions. We use simulation based optimisation 
 methods\,  mainly Monte Carlo and Markov Chain Monte Carlo\, in order to o
 btain solution in the general case.  We study the optimal design problem f
 or inference based on partial observations of random graphs by employing d
 ata augmentation technique. In particular\, we consider inference and opti
 mal design problems for finite open clusters from bond percolation on the 
 integer lattices and derive a range of both numerical and analytical resul
 ts for these graphs. (Our motivation here is that open clusters in bond pe
 rcolation may be seen as final outbreaks of an SIR epidemic with constant 
 infectious times.)  We introduce inner-outer design plots by considering a
  bounded region of the lattice  and deleting some of the lattice nodes wit
 hin this region and show that the 'mostly populated' designs are not neces
 sarily optimal in the case of incomplete observations under both progressi
 ve and instructive design scenarios. Some of the obtained results may gene
 ralise to other lattices.\n
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR