Handbook of Markov Chain Monte Carlo

2011/05/10 by Radford M. Neal, Steve Brooks, Andrew Gelman +2 · 1 voice · 16 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #physics.comp-ph #stat.CO

paper · pdf · doi:10.1201/b10905

openalex publication_date 2011/05/10 · arxiv published 2012/06/09 · arxiv updated 2012/06/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though originating in physics, Hamiltonian dynamics can be applied to most problems with continuous state spaces by simply introducing fictitious "momentum" variables. A key to its usefulness is that Hamiltonian dynamics preserves volume, and its trajectories can thus be used to define complex mappings without the need to account for a hard-to-compute Jacobian factor - a property that can be exactly maintained even when the dynamics is approximated by discretizing time. In this review, I discuss theoretical and practical aspects of Hamiltonian Monte Carlo, and present some of its variations, including using windows of states for deciding on acceptance or rejection, computing trajectories using fast approximations, tempering during the course of a trajectory to handle isolated modes, and short-cut methods that prevent useless trajectories from taking much computation time.

Citations

• The Short-Cut Metropolis Method
• Annealed Importance Sampling

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Discussions

• MCMC using Hamiltonian dynamics (2012) [hn, 2 points, 0 comments]