Publication:
Geometric integrators and the Hamiltonian Monte Carlo method

Thumbnail Image
Identifiers
URI: https://hdl.handle.net/10016/32602
ISSN: 0962-4929
DOI: https://doi.org/10.1017/S0962492917000101
UXXI: AR/0000021474
Files
Geometric_AN_2018_ps.pdf (2.72 MB)
Publication date
2018-05-01
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Cambridge University Press
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
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.
Description
Keywords
Bibliographic citation
Bou-Rabee, N. & Sanz-Serna, J. M. (2018). Geometric integrators and the Hamiltonian Monte Carlo method. Acta Numerica, vol. 27, pp. 113–206.
Collections
DM - Artículos de Revistas