Piecewise-deterministic Markov chain Monte Carlo

07.12.2018, 10:15-11:45  –  Haus 28, Raum 0.108
SFB-Kolloquium

Arnaud Doucet (Oxford University)

A novel class of continuous-time non-reversible Markov chain Monte Carlo (MCMC) based on piecewise-deterministic 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 schemes enjoy remarkable properties including the ability to update only a subset othe 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. The deterministic dynamics used so far do not exploit the geometry of the target. Moroever, exact simulation of the event times is feasible for an important yet restricted class of problems.
In this talk, I will show that it is possible to introduce discrete-time non-reversible algorithms which address these shortcomings and still enjoy the remarkable properties of the continuous-time algorithms. I will demonstrate the performance on these schemes on a variety of applications including Bayesian inference for big data and Bayesian inference for high-dimensional graphical models.