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SUMMARY:Optimal scaling of the random walk Metropolis - Christopher Sherlo
 ck\, Dept of Maths &amp\; Statistics\, Lancaster University
DTSTART:20091021T131500Z
DTEND:20091021T141500Z
UID:TALK19610@talks.cam.ac.uk
CONTACT:Rachel Fogg
DESCRIPTION:The random walk Metropolis (RWM) is one of the most commonly u
 sed Metropolis-Hastings algorithms\, and choosing the appropriate scaling 
 for the proposal is an important practical problem. Previous theoretical\n
 approaches have focussed on high-dimensional algorithms and have revolved 
 around a diffusion approximation of the trajectory. For certain specific c
 lasses of targets it has been possible to show that the algorithm is optim
 al when the acceptance rate is approximately 0.234.\n\nWe develop a novel 
 approach which avoids the need for diffusion limits. Focussing on spherica
 lly symmetric targets\, it is possible to derive simple exact formulae for
  efficiency and acceptance rate for a "real" RWM algorithm\, as opposed to
  a limit process. The limiting behaviour of these formulae can then be exp
 lored. This in some sense "simpler" approach allows important general intu
 itions as to when and why the 0.234 rule holds\, when the rule fails\, and
  what may happen when it does fail. By extending the theory to include ell
 iptically symmetric targets we obtain further intuitions about the role of
  the proposal's shape.
LOCATION:LR4\, Engineering\, Department of
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