IRREDUCIBILITY AND GEOMETRIC ERGODICITY OF HAMILTONIAN MONTE CARLO

• 成果类型: Article
• 署名作者: Durmus, Alain; Moulines, Eric; Saksman, Eero
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); HSE University (National Research University Higher School of Economics); University of Helsinki
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1941
• 发表日期: 2020
• 页码: 3545-3564
• 关键词: convergence; hastings

摘要

Hamiltonian Monte Carlo (HMC) is currently one of the most popular Markov Chain Monte Carlo algorithms to sample smooth distributions over continuous state space. This paper discusses the irreducibility and geometric ergodicity of the HMC algorithm. We consider cases where the number of steps of the Stormer-Verlet integrator is either fixed or random. Under mild conditions on the potential U associated with target distribution pi, we first show that the Markov kernel associated to the HMC algorithm is irreducible and positive recurrent. Under more stringent conditions, we then establish that the Markov kernel is Harris recurrent. We provide verifiable conditions on U under which the HMC sampler is geometrically ergodic. Finally, we illustrate our results on several examples.