Piecewise Deterministic Markov Processes (PDMPs) provide a powerful framework for continuous-time Monte Carlo, with the Bouncy Particle Sampler (BPS) as a prominent example. Recent advances through the Metropolised PDMP framework allow local adaptivity in step size and effective path length, the latter acting as a refreshment rate. However, current PDMP samplers cannot adapt to local changes in the covariance structure of the target distribution. We extend BPS by introducing a position-dependent velocity distribution that varies with the local covariance structure of the target. Building on ideas from Riemannian Manifold Hamiltonian Monte Carlo and its velocity-based variant, Lagrangian Dynamical Monte Carlo, we construct a PDMP for which changes in the metric trigger additional velocity update events. Using a metric derived from the target Hessian, the resulting algorithm adapts to the local covariance structure. Through a series of controlled experiments, we provide practical guidance on when the proposed covariance-adaptive BPS should be preferred over standard PDMP algorithms.

翻译：分段确定性马尔可夫过程为连续时间蒙特卡洛方法提供了一个强大的框架，其中弹跳粒子采样器是一个突出的例子。通过Metropolised PDMP框架的最新进展，允许在步长和有效路径长度上进行局部自适应，后者充当刷新率。然而，当前的PDMP采样器无法适应目标分布协方差结构的局部变化。我们通过引入一个依赖于位置的速度分布来扩展BPS，该速度分布随目标的局部协方差结构而变化。基于黎曼流形哈密顿蒙特卡洛及其基于速度的变体——拉格朗日动力学蒙特卡洛的思想，我们构建了一个PDMP，其中度量的变化会触发额外的速度更新事件。使用从目标Hessian导出的度量，所得算法能够适应局部协方差结构。通过一系列受控实验，我们为所提出的协方差自适应BPS何时应优于标准PDMP算法提供了实用指导。