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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Monte Carlo sampling with integrator snippets - Ch
 ristophe Andrieu (University of Bristol)
DTSTART;TZID=Europe/London:20240719T143000
DTEND;TZID=Europe/London:20240719T153000
UID:TALK219076AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/219076
DESCRIPTION:Assume interest is in sampling from a probability 
 distribution &mu\; defined on (Z\,Z). We develop a
  framework to construct sampling algorithms taking
  full advantage of numerical integrators of ODEs\,
  say &psi\; : Z&rarr\; Z for one integration step\
 , to explore &mu\;&nbsp\; efficiently and robustly
 . The popular Hybrid/Hamiltonian Monte Carlo (HMC)
  algorithm [duane1987hybrid\, neal2011mcmc] and it
 s derivatives are example of such a use of numeric
 al integrators. However\, we show how the potentia
 l of integrators can be exploited beyond current i
 deas and HMC sampling in order to take into accoun
 t aspects of the geometry of the target distributi
 on. A key idea is the notion of integrator snippet
 \, a fragment of the orbit of an ODE numerical int
 egrator &psi\; \, and its associate probability di
 stribution &mu\; &oline\;\, which takes the form o
 f a mixture of distributions derived from &mu\;&nb
 sp\; and &psi\; . Exploiting properties of mixture
 s we show how samples from &mu\; &oline\; can be u
 sed to estimate expectations with respect to &mu\;
  . We focus here primarily on Sequential Monte Car
 lo (SMC) algorithms\, but the approach can be used
  in the context of Markov chain Monte Carlo algori
 thms as discussed at the end of the manuscript. We
  illustrate performance of these new algorithms th
 rough numerical experimentation and provide prelim
 inary theoretical results supporting observed perf
 ormance.\n&nbsp\;\n&nbsp\;
LOCATION:External
CONTACT:
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