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The Barker proposal: Combining robustness and efficiency in gradient-based MCMC

Livingstone, S; Zanella, G; (2022) The Barker proposal: Combining robustness and efficiency in gradient-based MCMC. Journal of the Royal Statistical Society Statistical Methodology: Series B 10.1111/rssb.12482. (In press). Green open access

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Abstract

There is a tension between robustness and efficiency when designing Markov chain Monte Carlo (MCMC) sampling algorithms. Here we focus on robustness with respect to tuning parameters, showing that more sophisticated algorithms tend to be more sensitive to the choice of step-size parameter and less robust to heterogeneity of the distribution of interest. We characterise this phenomenon by studying the behaviour of spectral gaps as an increasingly poor step-size is chosen for the algorithm. Motivated by these considerations, we propose a novel and simple gradient-based MCMC algorithm, inspired by the classical Barker accept-reject rule, with improved robustness properties. Extensive theoretical results, dealing with robustness to tuning, geometric ergodicity and scaling with dimension, suggest that the novel scheme combines the robustness of simple schemes with the efficiency of gradient-based ones. We show numerically that this type of robustness is particularly beneficial in the context of adaptive MCMC, giving examples where our proposed scheme significantly outperforms state-of-the-art alternatives.

Type: Article
Title: The Barker proposal: Combining robustness and efficiency in gradient-based MCMC
Open access status: An open access version is available from UCL Discovery
DOI: 10.1111/rssb.12482
Publisher version: https://doi.org/10.1111/rssb.12482
Language: English
Additional information: © 2022 The Authors.Journal of the Royal Statistical Society: Series B (Statistical Methodology) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Keywords: adaptive tuning, Bayesian computation, MCMC, Metropolis–Hastings, spectral gap
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10136480
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