A fresh take on 'Barker dynamics' for MCMC

TL;DR

This paper thoroughly analyzes Barker dynamics in MCMC, deriving it from first principles, and demonstrates its robustness and effectiveness on complex, skewed logistic regression problems.

Contribution

It provides a full derivation of Barker dynamics from first principles and situates it within continuous-time Markov jump processes.

Findings

Barker dynamics is robust to irregular, skewed target distributions.

The method performs well on ill-conditioned logistic regression.

The derivation clarifies the theoretical foundations of Barker-based MCMC.

Abstract

We study a recently introduced gradient-based Markov chain Monte Carlo method based on 'Barker dynamics'. We provide a full derivation of the method from first principles, placing it within a wider class of continuous-time Markov jump processes. We then evaluate the Barker approach numerically on a challenging ill-conditioned logistic regression example with imbalanced data, showing in particular that the algorithm is remarkably robust to irregularity (in this case a high degree of skew) in the target distribution.