Piecewise Deterministic Markov Chain Monte Carlo

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. However, several important problems remain open. 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 methods and prevents the development of a generic software implementation. In this paper, we introduce novel MCMC methods addressing these limitations by bringing together piecewise deterministic Markov processes, Hamiltonian dynamics and slice sampling. We propose novel continuous-time algorithms relying on exact Hamiltonian flows and novel discrete-time algorithms which can exploit complex dynamics such as approximate Hamiltonian dynamics arising from symplectic integrators. We demonstrate the performance of these schemes on a variety of applications.