A0819
Title: Fluid limit of piecewise deterministic Monte Carlo methods
Authors: Kengo Kamatani - ISM (Japan) [presenting]
Joris Bierkens - Delft Institute of Applied Mathematics (Netherlands)
Gareth Roberts - University of Warwick (United Kingdom)
Sanket Agrawal - University of Warwick (United Kingdom)
Abstract: Piecewise deterministic Markov processes (PDMPs) provide the basis for several continuous-time Monte Carlo algorithms, including the bouncy particle sampler (BPS) and the ZigZag process. Their transient phase, meaning the movement from a low-density start to a high-density region, is studied under a convex potential. By combining fluid limits with an averaging decomposition of the generator into fast (nonergodic) and slow parts, the stochastic dynamics are approximated with deterministic ordinary differential equations. For Gaussian targets, BPS and ZigZag require the same early-stage cost as the random-walk Metropolis (RWM). For heavier-tailed targets, well-implemented PDMPs can outperform RWM, and certain event-chain variants achieve dimension-free mixing during the transient phase. These results clarify early behavior and guide the application of PDMP-based Monte Carlo methods to large-scale inference.
