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December 2020 Recycling Intermediate Steps to Improve Hamiltonian Monte Carlo
Akihiko Nishimura, David Dunson
Bayesian Anal. 15(4): 1087-1108 (December 2020). DOI: 10.1214/19-BA1171

Abstract

Hamiltonian Monte Carlo (HMC) and related algorithms have become routinely used in Bayesian computation. In this article, we present a simple and provably accurate method to improve the efficiency of HMC and related algorithms with essentially no extra computational cost. This is achieved by recycling the intermediate states along simulated trajectories of Hamiltonian dynamics. Standard algorithms use only the end points of trajectories, wastefully discarding all the intermediate states. Compared to the alternative methods for utilizing the intermediate states, our algorithm is simpler to apply in practice and requires little programming effort beyond the usual implementations of HMC and related algorithms. Our algorithm applies straightforwardly to the no-U-turn sampler, arguably the most popular variant of HMC. Through a variety of experiments, we demonstrate that our recycling algorithm yields substantial computational efficiency gains.

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Akihiko Nishimura. David Dunson. "Recycling Intermediate Steps to Improve Hamiltonian Monte Carlo." Bayesian Anal. 15 (4) 1087 - 1108, December 2020. https://doi.org/10.1214/19-BA1171

Information

Published: December 2020
First available in Project Euclid: 26 October 2019

Digital Object Identifier: 10.1214/19-BA1171

Keywords: Bayesian inference , Hamiltonian Monte Carlo , Markov chain Monte Carlo , multi-proposal , Rao-Blackwellization

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Vol.15 • No. 4 • December 2020
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