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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:title tba - Tony Lelievre (ENPC - École des Ponts
ParisTech)
DTSTART;TZID=Europe/London:20191120T135000
DTEND;TZID=Europe/London:20191120T143000
UID:TALK135037AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/135037
DESCRIPTION:Various applications require the sampling of
probability measures restricted to submanifolds d
efined as the level set of some functions\, in par
ticular in computational statistical physics. We w
ill present recent results on so-called Hybrid Mon
te Carlo methods\, which consists in adding an ext
ra momentum variable to the state of the system\,
and discretizing the associated Hamiltonian dynami
cs with some stochastic perturbation in the extra
variable. In order to avoid biases in the invarian
t probability measures sampled by discretizations
of these stochastically perturbed Hamiltonian dyna
mics\, a Metropolis rejection procedure can be con
sidered. The so-obtained scheme belongs to the cla
ss of generalized Hybrid Monte Carlo (GHMC) algori
thms\, and we will discuss how to ensure that the
sampling method is unbiased in practice.
References:
- T. Leliè\;vre\, M. Rousset
and G. Stoltz\, Langevin dynamics with constraint
s and computation of free energy differences\, Mat
hematics of Computation\, 81(280)\, 2012.
- T.
Leliè\;vre\, M. Rousset and G. Stoltz\, Hyb
rid Monte Carlo methods for sampling probability m
easures on submanifolds\, to appear in Numerische
Mathematik\, 2019.
- E. Zappa\, M. Holmes-Cerf
on\, and J. Goodman. Monte Carlo on manifolds: sam
pling densities and integrating functions. Communi
cations in Pure and Applied Mathematics\, 71(12)\,
2018.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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