Geometric integrators and the Hamiltonian Monte Carlo method

Nawaf Bou-Rabee, J. M. Sanz-Serna

Research output: Contribution to journalReview articlepeer-review

45 Scopus citations


This paper surveys in detail the relations between numerical integration and the Hamiltonian (or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies in the numerical integrations, these should be performed as efficiently as possible. However, HMC requires methods that have the geometric properties of being volume-preserving and reversible, and this limits the number of integrators that may be used. On the other hand, these geometric properties have important quantitative implications for the integration error, which in turn have an impact on the acceptance rate of the proposal. While at present the velocity Verlet algorithm is the method of choice for good reasons, we argue that Verlet can be improved upon. We also discuss in detail the behaviour of HMC as the dimensionality of the target distribution increases.

Original languageEnglish (US)
Pages (from-to)113-206
Number of pages94
JournalActa Numerica
StatePublished - May 1 2018

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Mathematics(all)


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