Piecewise-deterministic Markov process (PDMP) samplers constitute a state-of-the-art Markov chain Monte Carlo paradigm in Bayesian computation, with examples including the zig-zag and bouncy particle sampler (bps). Recent work on the zig-zag has indicated its connection to Hamiltonian Monte Carlo (HMC), a version of the Metropolis algorithm that exploits Hamiltonian dynamics. Here we establish that, in fact, the connection between the two paradigms extends far beyond the specific instance. The key lies in (1) the fact that any time-reversible deterministic dynamics provides a valid Metropolis proposal and (2) how PDMPs' characteristic velocity changes constitute an alternative to the usual acceptance-rejection. We turn this observation into a rigorous framework for constructing rejection-free Metropolis proposals based on bouncy Hamiltonian dynamics which simultaneously possess Hamiltonian-like properties and generate discontinuous trajectories similar in appearance to PDMPs. When combined with periodic refreshment of the inertia, the dynamics converge strongly to PDMP equivalents in the limit of increasingly frequent refreshment. We demonstrate the practical implications of this new framework with a sampler based on a bouncy Hamiltonian dynamics closely related to the bps. The resulting sampler exhibits competitive performance on challenging real-data posteriors involving tens of thousands of parameters. As the sampler of choice in modern probabilistic programming languages, HMC plays a critical role in applied Bayesian modeling; by generalizing the paradigm and elucidating its connection to the leading competitor, our framework opens up opportunities for cross-pollination and innovation to further scale Bayesian inference.

翻译：分段确定性马尔可夫过程采样器构成了贝叶斯计算中先进的马尔可夫链蒙特卡罗范式，其典型实例包括 zig-zag 采样器与弹跳粒子采样器。近期关于 zig-zag 的研究揭示了其与哈密顿蒙特卡罗的联系——后者是一种利用哈密顿动力学的 Metropolis 算法变体。本文证明，这两种范式间的关联远不止于特定实例。关键在于：（1）任何时间可逆的确定性动力学均可构造有效的 Metropolis 提案；（2）PDMP 特有的速度切换机制构成了对传统接受-拒绝步骤的替代方案。基于此观察，我们建立了基于弹跳哈密顿动力学的拒绝式 Metropolis 提案的严格构建框架，该框架同时具备类哈密顿特性并生成与 PDMP 外观相似的不连续轨迹。当结合惯量的周期性重置时，该动力学在重置频率趋于无穷的极限下强收敛于等效的 PDMP。我们通过一个与 bps 密切相关的弹跳哈密顿动力学采样器展示了新框架的实际意义。该采样器在涉及数万个参数的复杂实际数据后验分布上表现出具有竞争力的性能。作为现代概率编程语言中的首选采样器，HMC 在应用贝叶斯建模中起着关键作用；通过推广该范式并阐明其与主要竞争方法的联系，我们的框架为交叉融合与创新提供了新机遇，从而进一步扩展贝叶斯推断的适用范围。