2016/04/04 by Akihiko Nishimura, David Dunson, David B. Dunson +2 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Compressibility #Computation (stat.CO) #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #Elasticity and Material Modeling #FOS: Computer and information sciences #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical analysis #Mathematics #Mechanics #Monte Carlo method #Physics #Statistical physics #Statistics #Trajectory #Variable (mathematics) #physics.comp-ph #stat.CO
paper · pdf · doi:10.48550/arxiv.1604.00889
published in arXiv (Cornell University) (Cornell University) · 10 pages, 3 figures
arxiv created 2016/04/04 · openalex publication_date 2016/04/04 · arxiv updated 2016/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hybrid Monte Carlo (HMC) generates samples from a prescribed probability distribution in a configuration space by simulating Hamiltonian dynamics, followed by the Metropolis (-Hastings) acceptance/rejection step. Compressible HMC (CHMC) generalizes HMC to a situation in which the dynamics is reversible but not necessarily Hamiltonian. This article presents a framework to further extend the algorithm. Within the existing framework, each trajectory of the dynamics must be integrated for the same amount of (random) time to generate a valid Metropolis proposal. Our generalized acceptance/rejection mechanism allows a more deliberate choice of the integration time for each trajectory. The proposed algorithm in particular enables an effective application of variable step size integrators to HMC-type sampling algorithms based on reversible dynamics. The potential of our framework is further demonstrated by another extension of HMC which reduces the wasted computations due to unstable numerical approximations and corresponding rejected proposals.