Hug and Hop: a discrete-time, non-reversible Markov chain Monte Carlo algorithm
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We introduced the Hug and Hop Markov chain Monte Carlo algorithm for estimating expectations with respect to an intractable distribution π. The algorithm alternates between two kernels: Hug and Hop. Hug is a non-reversible kernel that uses repeated applications of the bounce mechanism from the recently proposed Bouncy Particle Sampler to produce a proposal point far from the current position, yet on almost the same contour of the target density, leading to a high acceptance probability. Hug is complemented by Hop, which deliberately proposes jumps between contours and has an efficiency that degrades very slowly with increasing dimension. There are many parallels between Hug and Hamiltonian Monte Carlo (HMC) using a leapfrog intergator, including an O(δ^2) error in the integration scheme, however Hug is also able to make use of local Hessian information without requiring implicit numerical integration steps, improving efficiency when the gains in mixing outweigh the additional computational costs. We test Hug and Hop empirically on a variety of toy targets and real statistical models and find that it can, and often does, outperform HMC on the exploration of components of the target.
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