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arXiv · 1909.07962

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

Nawaf Bou-Rabee·Andreas Eberle
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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.

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Nawaf Bou-Rabee, Andreas Eberle. 2019-09-17. Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions. https://doi.org/10.1007/s40072-020-00175-6

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