Summary Most Markov chain Monte Carlo methods operate in discrete time and are reversible with respect to the target probability. Nevertheless, it is now understood that the use of nonreversible Markov chains can be beneficial in many contexts. In particular, the recently proposed bouncy particle sampler leverages a continuous-time and nonreversible Markov process, and empirically shows state-of-the-art performance when used to explore certain probability densities; however, its implementation typically requires the computation of local upper bounds on the gradient of the log target density. We present the discrete bouncy particle sampler, a general algorithm based on a guided random walk, a partial refreshment of direction and a delayed-rejection step. We show that the bouncy particle sampler can be understood as a scaling limit of a special case of our algorithm. In contrast to the bouncy particle sampler, implementing the discrete bouncy particle sampler only requires pointwise evaluation of the target density and its gradient. We propose extensions of the basic algorithm for situations when the exact gradient of the target density is not available. In a Gaussian setting, we establish a scaling limit for the radial process as the dimension increases to infinity. We leverage this result to obtain the theoretical efficiency of the discrete bouncy particle sampler as a function of the partial-refreshment parameter, which leads to a simple and robust tuning criterion. A further analysis in a more general setting suggests that this tuning criterion applies more generally. Theoretical and empirical efficiency curves are then compared for different targets and algorithm variations.

中文翻译：

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离散弹性粒子采样器

总结 大多数马尔可夫链蒙特卡罗方法在离散时间运行，并且相对于目标概率是可逆的。尽管如此，现在可以理解的是，使用不可逆马尔可夫链在许多情况下都是有益的。特别是，最近提出的弹性粒子采样器利用了连续时间和不可逆的马尔可夫过程，并在用于探索某些概率密度时凭经验展示了最先进的性能；然而，它的实现通常需要计算对数目标密度梯度的局部上限。我们提出了离散弹性粒子采样器，这是​​一种基于引导随机游走、方向部分刷新和延迟拒绝步骤的通用算法。我们表明，弹性粒子采样器可以理解为我们算法特殊情况的缩放限制。与弹性粒子采样器相比，实现离散弹性粒子采样器只需要对目标密度及其梯度进行逐点评估。我们建议在目标密度的精确梯度不可用的情况下扩展基本算法。在高斯设置中，随着维度增加到无穷大，我们为径向过程建立了缩放限制。我们利用这个结果来获得离散弹性粒子采样器的理论效率作为部分刷新参数的函数，这导致了一个简单而稳健的调整标准。在更一般的环境中进行的进一步分析表明，这种调整标准更普遍适用。