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Zigzag and other piecewise deterministic Markov process samplers haveattracted significant interest for their non-reversibility and other appealingproperties for Bayesian posterior computation. Hamiltonian Monte Carlo isanother state-of-the-art sampler, exploiting fictitious momentum to guideMarkov chains through complex target distributions. In this article, we uncovera remarkable connection between the zigzag sampler and a variant of HamiltonianMonte Carlo based on Laplace-distributed momentum. The position and velocitycomponent of the corresponding Hamiltonian dynamics travels along a zigzag pathparalleling the Markovian zigzag process; however, the dynamics isnon-Markovian in the position-velocity space as the momentum component encodesnon-immediate pasts. This information is partially lost during a momentumrefreshment step, in which we preserve its direction but re-sample magnitude.In the limit of increasingly frequent momentum refreshments, we prove thatHamiltonian zigzag converges strongly to its Markovian counterpart. Thistheoretical insight suggests that, when retaining full momentum information,Hamiltonian zigzag can better explore target distributions with highlycorrelated parameters by suppressing the diffusive behavior of Markovianzigzag. We corroborate this intuition by comparing performance of the twozigzag cousins on high-dimensional truncated multivariate Gaussians, includinga 11,235-dimensional target arising from a Bayesian phylogenetic multivariateprobit model applied to HIV virus data.

Hamiltonian zigzag sampler got more momentum than its Markovian counterpart: Equivalence of two zigzags under a momentum refreshment limit