On the Geometric Ergodicity of Hamiltonian Monte Carlo

arXiv:1601.08057 · stat.CO, stat.ME, stat.ML · Submitted 2016-01-29 · Read on arXiv

stat.CO, stat.ME, stat.ML

Submitted: 2016-01-29

Updated: 2026-09-08

Comments: 29 pages + supplement (included in arXival as Appendix), 1 figure. Corrigendum related to Theorem 5.14 and Corollary 2.3 included as Appendix D

Journal ref: Bernoulli 25(4A) (2019), 3109-3138

DOI: 10.3150/18-BEJ1083

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Lyapunov function — 7× in this paper · explained in 2 episodes
• Langevin Dynamics — 5× in this paper · explained in 2 episodes
• Inverse Problem — 2× in this paper · explained in 2 episodes
• Wasserstein Distance — 2× in this paper · explained in 4 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Hilbert Space — 1× in this paper · explained in 2 episodes

Sources

• Identifying the Optimal Integration Time in Hamiltonian Monte Carlo
• Randomized Hamiltonian Monte Carlo
• On the convergence of Hamiltonian Monte Carlo

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