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SUMMARY:Multilevel Monte Carlo Methods - Robert Scheichl (University of Ba
 th)
DTSTART:20180112T090000Z
DTEND:20180112T100000Z
UID:TALK97528@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Multilevel Monte Carlo (MLMC) is a variance reduction techniqu
 e for stochastic simulation and Bayesian inference which greatly reduces t
 he computational cost of standard Monte Carlo approaches by employing chea
 p\, coarse-scale models with lower fidelity to carry out the bulk of the s
 tochastic simulations\, while maintaining the overall accuracy of the fine
  scale model through a small number of well-chosen high fidelity  simulati
 ons.  In this talk\, I will first review the ideas behind the approach and
  discuss a number of applications and extensions that illustrate the gener
 ality of the approach. The multilevel Monte Carlo method (in its practical
  form) has originally been introduced and popularised about 10 years ago b
 y Mike Giles for stochastic differential equations in mathematical finance
  and has attracted a lot of interest in the context of uncertainty quantif
 ication of physical systems modelled by partial differential equations (PD
 Es). The underlying idea had actually been discovered 10 years earlier in 
 1998\, in an information-theoretical paper by Stefan Heinrich\, but had re
 mained largely unknown until 2008. In recent years\, there has been an exp
 losion of activity and its application has been extended\, among others\, 
 to biological/chemical reaction networks\, plasma physics\, interacting pa
 rticle systems as well as to nested simulations.  More importantly for thi
 s community\, the approach has also been extended to Markov chain Monte Ca
 rlo\, 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 tractable methodology for Bayesian inference
  in high-dimensional models constrained by PDEs and demonstrate the potent
 ial on a toy problem in the context of Metropolis-Hastings MCMC. Finally\,
  I will finish the talk with some perspectives beyond the classical MLMC f
 ramework\, in particular using sample-dependent model hierarchies and a po
 steriori error estimators and extending the classical discrete\, level-bas
 ed approach to a new Continuous Level Monte Carlo method.
LOCATION:Seminar Room 1\, Newton Institute
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