2017/06/30 by Julien Stoehr, Stoehr, Julien, Alan P. Benson +3 · 1 citation
Mathematics · Physics and Astronomy · #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.1706.10096
openalex publication_date 2017/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hamiltonian Monte Carlo (HMC) has been progressively incorporated within the statistician's toolbox as an alternative sampling method in settings when standard Metropolis-Hastings is inefficient. HMC generates a Markov chain on an augmented state space with transitions based on a deterministic differential flow derived from Hamiltonian mechanics. In practice, the evolution of Hamiltonian systems cannot be solved analytically, requiring numerical integration schemes. Under numerical integration, the resulting approximate solution no longer preserves the measure of the target distribution, therefore an accept-reject step is used to correct the bias. For doubly-intractable distributions -- such as posterior distributions based on Gibbs random fields -- HMC suffers from some computational difficulties: computation of gradients in the differential flow and computation of the accept-reject proposals poses difficulty. In this paper, we study the behaviour of HMC when these quantities are replaced by Monte Carlo estimates.