Title: Piecewise deterministic Markov chain Monte Carlo for Bayesian computation
Authors: Arnaud Doucet - University of Oxford (United Kingdom) [presenting]
Alexandre Bouchard - University of British Columbia (Canada)
George Deligiannidis - King's College London (United Kingdom)
Abstract: 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, these algorithms 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. We introduce novel MCMC methods addressing these shortcomings by bringing together piecewise deterministic Markov processes, Hamiltonian dynamics and slice sampling. We present 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 Bayesian inference tasks.