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SUMMARY:title tba - Tony Lelievre (ENPC - École des Ponts ParisTech)
DTSTART:20191120T135000Z
DTEND:20191120T143000Z
UID:TALK135037@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Various applications require the sampling of probability
  measures restricted to submanifolds defined as the level set of some func
 tions\, in particular in computational statistical physics. We will presen
 t recent results on so-called Hybrid Monte Carlo methods\, which consists 
 in adding an extra momentum variable to the state of the system\, and disc
 retizing the associated Hamiltonian dynamics with some stochastic perturba
 tion in the extra variable. In order to avoid biases in the invariant prob
 ability measures sampled by discretizations of these stochastically pertur
 bed Hamiltonian dynamics\, a Metropolis rejection procedure can be conside
 red. The so-obtained scheme belongs to the class of generalized Hybrid Mon
 te Carlo (GHMC) algorithms\, and we will discuss how to ensure that the sa
 mpling method is unbiased in practice.<br> <br> References:<br> - T. Leli&
 egrave\;vre\, M. Rousset and G. Stoltz\, Langevin dynamics with constraint
 s and computation of free energy differences\, Mathematics of Computation\
 , 81(280)\, 2012.<br> - T. Leli&egrave\;vre\, M. Rousset and G. Stoltz\, H
 ybrid Monte Carlo methods for sampling probability measures on submanifold
 s\, to appear in Numerische Mathematik\, 2019.<br> - E. Zappa\, M. Holmes-
 Cerfon\, and J. Goodman. Monte Carlo on manifolds: sampling densities and 
 integrating functions. Communications in Pure and Applied Mathematics\, 71
 (12)\, 2018.</span><br><br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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