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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Efficient Monte Carlo for high excursions of Gauss
ian random fields - Adler\, RJ\, Blanchet\, JH\, L
iu\, J (Israel\; Columbia\; Columbia)
DTSTART;TZID=Europe/London:20100622T170500
DTEND;TZID=Europe/London:20100622T173000
UID:TALK25322AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/25322
DESCRIPTION:We focus on the design and analysis of efficient M
onte Carlo methods for computing the tail probabil
ity at level b of the maximum of a Gaussian random
field and the associated conditional expectations
of the field given excursions at levels larger th
an b. Nave Monte Carlo takes an exponential comput
ational cost in b to estimate such tail probabilit
ies and associated conditional expectations with p
rescribed relative accuracy. In contrast\, our Mon
te Carlo procedures exhibit at the most polynomial
complexity in b assuming only that the mean and c
ovariance functions are Holder continuous. In pres
ence of more regularity conditions\, such as homog
eneity and smoothness\, the complexity results can
be further improved to constant. Central to the d
esign of Monte Carlo scheme and its efficiency ana
lysis is a change of measure that is NOT of the tr
aditional exponential\ntilting form. This change o
f measure admits different representations that li
nk the analysis of Monte Carlo methods to the rand
om fields geometry. This feature is appealing to b
oth simulation design and theoretical development
of random fields. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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