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SUMMARY:A theoretical and methodological discussion of nested sampling - N
 icolas Chopin (Bristol)
DTSTART:20080118T140000Z
DTEND:20080118T150000Z
UID:TALK9975@talks.cam.ac.uk
CONTACT:8048
DESCRIPTION:Nested sampling is a novel simulation method for approximating
  marginal likelihoods\, proposed by \\cite{Skilling:2007a\,Skilling:2007b}
 . We establish that nested sampling leads to an error that vanishes at the
  standard Monte Carlo rate N-1/2\, where N is a tuning parameter that is p
 roportional to the computational effort\, and that this error is asymptoti
 cally Gaussian. We show that the corresponding asymptotic variance typical
 ly grows linearly with the dimension of the parameter.  We use these resul
 ts to discuss the applicability and efficiency of nested sampling in reali
 stic problems\, including posterior distributions for mixtures. We propose
  an extension of nested sampling that makes it possible to avoid resorting
  to MCMC to obtain the simulated points. We study two alternative methods 
 for computing marginal likelihood\, which\, in contrast with nested sampli
 ng\, are based on draws from the posterior distribution and we conduct a c
 omparison with nested sampling on several realistic examples. \n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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