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SUMMARY:Monte Carlo sampling with integrator snippets - Christophe Andrieu
  (University of Bristol)
DTSTART:20240719T133000Z
DTEND:20240719T143000Z
UID:TALK219076@talks.cam.ac.uk
DESCRIPTION:Assume interest is in sampling from a probability distribution
  &mu\; defined on (Z\,Z). We develop a framework to construct sampling alg
 orithms taking full advantage of numerical integrators of ODEs\, say &psi\
 ; : Z&rarr\; Z for one integration step\, to explore &mu\;&nbsp\; efficien
 tly and robustly. The popular Hybrid/Hamiltonian Monte Carlo (HMC) algorit
 hm [duane1987hybrid\, neal2011mcmc] and its derivatives are example of suc
 h a use of numerical integrators. However\, we show how the potential of i
 ntegrators can be exploited beyond current ideas and HMC sampling in order
  to take into account aspects of the geometry of the target distribution. 
 A key idea is the notion of integrator snippet\, a fragment of the orbit o
 f an ODE numerical integrator &psi\; \, and its associate probability dist
 ribution &mu\; &oline\;\, which takes the form of a mixture of distributio
 ns derived from &mu\;&nbsp\; and &psi\; . Exploiting properties of mixture
 s we show how samples from &mu\; &oline\; can be used to estimate expectat
 ions with respect to &mu\; . We focus here primarily on Sequential Monte C
 arlo (SMC) algorithms\, but the approach can be used in the context of Mar
 kov chain Monte Carlo algorithms as discussed at the end of the manuscript
 . We illustrate performance of these new algorithms through numerical expe
 rimentation and provide preliminary theoretical results supporting observe
 d performance.\n&nbsp\;\n&nbsp\;
LOCATION:External
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