The Coordinate Sampler: A Non-Reversible Gibbs-like MCMC Sampler

Abstract

In this article, we derive a novel non-reversible, continuous-time Markov chain Monte Carlo (MCMC) sampler, called Coordinate Sampler, based on a piecewise deterministic Markov process (PDMP), which can be seen as a variant of the Zigzag sampler. In addition to proving a theoretical validation for this new sampling algorithm, we show that the Markov chain it induces exhibits geometrical ergodicity convergence, for distributions whose tails decay at least as fast as an exponential distribution and at most as fast as a Gaussian distribution. Several numerical examples highlight that our coordinate sampler is more efficient than the Zigzag sampler, in terms of effective sample size.

arXiv comment5 figures, 26 pages

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Cited by in corpus (3)

• On explicit $L^2$-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms
• Accelerated Sampling on Discrete Spaces with Non-Reversible Markov Processes
• Long-time behaviour of generalised Zig-Zag process