High-Dimensional Behaviour of Two Piecewise Deterministic Monte Carlo Algorithms: Efficiency Comparison & Asymptotic Variance Estimation
Piecewise deterministic Markov process (PDMP) samplers are attractive alternatives to Metropolis–Hastings methods, but their performance hinges on how partial velocity refreshment is implemented. We develop a high-dimensional scaling analysis to compare Forward Event-Chain Monte Carlo (FECMC) with the Bouncy Particle Sampler (BPS). For a standard Gaussian target, the (rescaled) negative log-density process converges to an Ornstein–Uhlenbeck limit with a diffusion coefficient strictly larger for FECMC than for optimally tuned BPS. The analysis implies that FECMC is asymptotically most efficient without global refreshment, and experiments show an approximately 15-fold gain in ESS per unit time. We also discuss an interesting application of our results to PDMP output analysis and diagnostics.