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