Split Hamiltonian Monte Carlo revisited

2022/07/15 by Fernando Casas, Casas, Fernando, J. M. Sanz‐Serna +3
Mathematics · Physics and Astronomy · #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2207.07516

openalex publication_date 2022/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Hamiltonian Monte Carlo (HMC) samplers based on splitting the Hamiltonian H as H₀(θ,p)+U₁(θ), where H₀ is quadratic and U₁ small. We show that, in general, such samplers suffer from stepsize stability restrictions similar to those of algorithms based on the standard leapfrog integrator. The restrictions may be circumvented by preconditioning the dynamics. Numerical experiments show that, when the H₀(θ,p)+U₁(θ) splitting is combined with preconditioning, it is possible to construct samplers far more efficient than standard leapfrog HMC.

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