  A novel class of non-reversible Markov chain Monte Carlo schemes relying on
continuous-time piecewise-deterministic Markov Processes has recently emerged.
In these algorithms, the state of the Markov process evolves according to a
deterministic dynamics which is modified using a Markov transition kernel at
random event times. These methods enjoy remarkable features including the
ability to update only a subset of the state components while other components
implicitly keep evolving and the ability to use an unbiased estimate of the
gradient of the log-target while preserving the target as invariant
distribution. However, they also suffer from important limitations. The
deterministic dynamics used so far do not exploit the structure of the target.
Moreover, exact simulation of the event times is feasible for an important yet
restricted class of problems and, even when it is, it is application specific.
This limits the applicability of these techniques and prevents the development
of a generic software implementation of them. We introduce novel MCMC methods
addressing these shortcomings. In particular, we introduce novel
continuous-time algorithms relying on exact Hamiltonian flows and novel
non-reversible discrete-time algorithms which can exploit complex dynamics such
as approximate Hamiltonian dynamics arising from symplectic integrators while
preserving the attractive features of continuous-time algorithms. We
demonstrate the performance of these schemes on a variety of applications.

Methodology