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SUMMARY:Hamiltonian Monte Carlo vs. event-chain Monte Carlo:  Synopsis\, b
 enchmarks\, prospects - Werner Krauth (ENS - Paris)
DTSTART:20241125T101500Z
DTEND:20241125T110500Z
UID:TALK221467@talks.cam.ac.uk
DESCRIPTION:Markov-chain Monte Carlo permeates all fields of science\, fro
 m physics to statistics and to the social disciplines. Reversible Markov c
 hains\, the great majority of Monte Carlo methods\, map the sampling of pr
 obability distributions onto the simulation of fictitious physical systems
  in thermal equilibrium. In physics\, thermal equilibrium is characterized
  by time-reversal invariance and the detailed-balance condition. It thus c
 omes as no surprise that reversible Markov chains\, such as the famous Met
 ropolis and heat-bath algorithms\, all satisfy detailed balance. In physic
 s\, again\, thermal equilibrium is characterized by diffusive\, local\, mo
 tion of particles.This slowness translates to the slow mixing and relaxati
 on dynamics of local reversible Markov chains\, and it affects most Markov
  chains used in practice.In this talk\, I confront diametrically opposite 
 strategies to overcome the slow diffusive motion of local\, reversible MCM
 C methods. One is Hamiltonian Monte Carlo\, a non-local yet reversible Mar
 kov chain\, and the other is event-chain Monte Carlo\, a class oflifted Ma
 rkov chains\, which are local yet non-reversible. In a simple one-dimensio
 nal continuum model of interacting particles\, I show that event-chain Mon
 te Carlo reaches better scaling of relaxation times than Hamiltonian Monte
  Carlo. I will connect this finding\, on the one hand\, to recent work on 
 a related lattice model\, the lifted TASEP (lifted totally asymmetric simp
 le exclusion model)\, which is exactly solvable through the Bethe ansatz\,
  and on the other hand to the "true" self-avoiding walk. I will finally di
 scuss applications to real-world problems\, where event-chain Monte Carlo 
 allows one to sample the Boltzmann distribution exp(-beta U) without evalu
 ating the energy U.
LOCATION:Seminar Room 1\, Newton Institute
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