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SUMMARY:Efficient Monte Carlo for high excursions of Gaussian random field
 s - Adler\, RJ\, Blanchet\, JH\, Liu\, J (Israel\; Columbia\; Columbia)
DTSTART:20100622T160500Z
DTEND:20100622T163000Z
UID:TALK25322@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We focus on the design and analysis of efficient Monte Carlo m
 ethods for computing the tail probability at level b of the maximum of a G
 aussian random field and the associated conditional expectations of the fi
 eld given excursions at levels larger than b. Nave Monte Carlo takes an ex
 ponential computational cost in b to estimate such tail probabilities and 
 associated conditional expectations with prescribed relative accuracy. In 
 contrast\, our Monte Carlo procedures exhibit at the most polynomial compl
 exity in b assuming only that the mean and covariance functions are Holder
  continuous. In presence of more regularity conditions\, such as homogenei
 ty and smoothness\, the complexity results can be further improved to cons
 tant. Central to the design of Monte Carlo scheme and its efficiency analy
 sis is a change of measure that is NOT of the traditional exponential\ntil
 ting form. This change of measure admits different representations that li
 nk the analysis of Monte Carlo methods to the random fields geometry. This
  feature is appealing to both simulation design and theoretical developmen
 t of random fields. \n
LOCATION:Seminar Room 1\, Newton Institute
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