Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions

Nawaf Bou-Rabee, Andreas Eberle

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We derive non-asymptotic quantitative bounds for convergence to equilibrium of the exact preconditioned Hamiltonian Monte Carlo algorithm (pHMC) on a Hilbert space. As a consequence, explicit and dimension-free bounds for pHMC applied to high-dimensional distributions arising in transition path sampling and path integral molecular dynamics are given. Global convexity of the underlying potential energies is not required. Our results are based on a two-scale coupling which is contractive in a carefully designed distance.

Original languageEnglish (US)
Pages (from-to)207-242
Number of pages36
JournalStochastics and Partial Differential Equations: Analysis and Computations
Volume9
Issue number1
DOIs
StatePublished - Mar 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Convergence to equilibrium
  • Coupling
  • Geometric integration
  • Hamiltonian Monte Carlo
  • Hilbert spaces
  • Hybrid Monte Carlo
  • Markov Chain Monte Carlo in infinite dimensions
  • Metropolis-Hastings

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