Chair: Hidetoshi Murakami (Tokyo University of Science, Japan)
The scaling limit analysis for Markov chain Monte Carlo methods has been developed over the last decades. The analysis identifies the rate of convergence to the limiting process, typically the Langevin diffusion process. Moreover, this analysis provides useful criteria for parameter tuning in Monte Carlo methods, as the limiting process is usually much simpler than the Markov chain Monte Carlo process and thus easier to optimise with respect to the tuning parameter. After the seminal work of Roberts et al. in 1997, many researchers have generalised the assumption and extended the results to more advanced methods. In the first half of this talk, we will review some basic scaling limit results for Markov chain Monte Carlo methods.
Recently, piecewise deterministic Markov processes have gained interest in the context of scalable Monte Carlo integration methods. Two examples of fundamental importance are the Bouncy Particle sampler and the Zig-Zag sampler. In this talk, we will determine the scaling limits for both algorithms. Finally, we discuss a criterion for the tuning parameter of the Bouncy Particle sampler.
The latter part is a joint work with J. Bierkens (TU Delft) and G. O. Roberts (Warwick).