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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Multilevel Monte Carlo Methods - Robert Scheichl (
University of Bath)
DTSTART;TZID=Europe/London:20180112T090000
DTEND;TZID=Europe/London:20180112T100000
UID:TALK97528AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/97528
DESCRIPTION:Multilevel Monte Carlo (MLMC) is a variance reduct
ion technique for stochastic simulation and Bayesi
an inference which greatly reduces the computation
al cost of standard Monte Carlo approaches by empl
oying cheap\, coarse-scale models with lower fidel
ity to carry out the bulk of the stochastic simula
tions\, while maintaining the overall accuracy of
the fine scale model through a small number of wel
l-chosen high fidelity simulations. In this talk
\, I will first review the ideas behind the approa
ch and discuss a number of applications and extens
ions that illustrate the generality of the approac
h. The multilevel Monte Carlo method (in its pract
ical form) has originally been introduced and popu
larised about 10 years ago by Mike Giles for stoch
astic differential equations in mathematical finan
ce and has attracted a lot of interest in the cont
ext of uncertainty quantification of physical syst
ems modelled by partial differential equations (PD
Es). The underlying idea had actually been discove
red 10 years earlier in 1998\, in an information-t
heoretical paper by Stefan Heinrich\, but had rema
ined largely unknown until 2008. In recent years\,
there has been an explosion of activity and its a
pplication has been extended\, among others\, to b
iological/chemical reaction networks\, plasma phys
ics\, interacting particle systems as well as to n
ested simulations. More importantly for this comm
unity\, the approach has also been extended to Mar
kov chain Monte Carlo\, sequential Monte Carlo and
other filtering techniques. In the second part of
the talk\, I will describe in more detail how the
MLMC framework can provide a computationally trac
table methodology for Bayesian inference in high-d
imensional models constrained by PDEs and demonstr
ate the potential on a toy problem in the context
of Metropolis-Hastings MCMC. Finally\, I will fini
sh the talk with some perspectives beyond the clas
sical MLMC framework\, in particular using sample-
dependent model hierarchies and a posteriori error
estimators and extending the classical discrete\,
level-based approach to a new Continuous Level Mo
nte Carlo method.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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