The ZigZag Process and Speeding Up (Giorgos Vasdekis)

16:00, November 8, Kennedy Seminar Room 2

 Abstract: Piecewise Deterministic Markov Processes have recently drawn the attention of the Markov Chain Monte Carlo community. The first reason for this is that, in general, one can simulate exactly the entire path of such a process. The second is that these processes are non-reversible, which sometimes leads to faster mixing.  One of the processes used to construct Piecewise Deterministic Algorithms is the ZigZag process. This process moves linearly in the space $\mathbb{R}^d$ in specific directions for a random period of time, changing direction one coordinate at a time. An important question related to these samplers is the existence of a Central Limit Theorem which is closely connected to the property of Geometric Ergodicity.  In this talk we will explain why the ZigZag Sampler is not Geometrically Ergodic when the target distribution has heavy tails and we will suggest how one could try to correct this by allowing the ZigZag process to speed up in certain regions.​