Piecewise deterministic Markov process samplers are attractive alternatives to Metropolis--Hastings algorithms. A central design question is how to incorporate partial velocity refreshment to ensure ergodicity without injecting excessive noise. Forward Event-Chain Monte Carlo (FECMC) is a generalization of the Bouncy Particle Sampler (BPS) that addresses this issue through a stochastic reflection mechanism, thereby reducing reliance on global refreshment moves. Despite promising empirical performance, its theoretical efficiency remains largely unexplored. We develop a high-dimensional scaling analysis for standard Gaussian targets and prove that the negative log-density (or potential) process of FECMC converges to an Ornstein--Uhlenbeck diffusion, under the same scaling as BPS. We derive closed-form expressions for the limiting diffusion coefficients of both methods by analyzing their associated radial momentum processes and solving the corresponding Poisson equations. These expressions yield a sharp efficiency comparison: the diffusion coefficient of FECMC is strictly larger than that of optimally tuned BPS, and the optimum for FECMC is attained at zero global refreshment. Specifically, they imply an approximately eightfold increase in effective sample size per event over optimal BPS. Numerical experiments confirm the predicted diffusion coefficients and show that the resulting efficiency gains remain substantial for a range of non-Gaussian targets. Finally, as an application of these results, we propose an asymptotic variance estimator for Piecewise deterministic Markov processes that becomes increasingly efficient in high dimensions by extracting information from the velocity variable.

翻译：分段确定性马尔可夫过程采样器是Metropolis–Hastings算法的有吸引力的替代方案。一个核心设计问题是如何引入部分速度更新以确保遍历性，同时避免注入过多噪声。前向事件链蒙特卡洛（FECMC）是弹跳粒子采样器（BPS）的推广，它通过随机反射机制解决这一问题，从而减少对全局更新操作的依赖。尽管其经验表现良好，其理论效率在很大程度上仍未得到探索。我们针对标准高斯目标发展了高维尺度分析，并证明在BPS相同的尺度下，FECMC的负对数密度（或势）过程收敛于Ornstein–Uhlenbeck扩散。通过分析两种方法相关的径向动量过程并求解相应的泊松方程，我们推导了二者极限扩散系数的闭式表达式。这些表达式提供了精确的效率比较：FECMC的扩散系数严格大于经最优调参的BPS，且FECMC的最优参数在全局更新率为零时达到。具体而言，这意味着在每次事件上，其有效样本量较最优BPS提升约八倍。数值实验证实了预测的扩散系数，并表明对于一系列非高斯目标，由此带来的效率提升依然显著。最后，作为这些结果的应用，我们提出了一种针对分段确定性马尔可夫过程的渐近方差估计器，该估计器通过从速度变量中提取信息，在高维情形下效率不断提升。