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In most sampling algorithms, including Hamiltonian Monte Carlo, transitionrates between states correspond to the probability of making a transition in asingle time step, and are constrained to be less than or equal to 1. We derivea Hamiltonian Monte Carlo algorithm using a continuous time Markov jumpprocess, and are thus able to escape this constraint. Transition rates in aMarkov jump process need only be non-negative. We demonstrate that the newalgorithm leads to improved mixing for several example problems, both byevaluating the spectral gap of the Markov operator, and by computingautocorrelation as a function of compute time. We release the algorithm as anopen source Python package.

A Markov Jump Process for More Efficient Hamiltonian Monte Carlo