A discrete bouncy particle sampler
A discrete bouncy particle sampler
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DOI：
10.1093/biomet/asab013
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发表时间：
2017-07
期刊：
影响因子：
2.7
通讯作者：
C. Sherlock;Alexandre Hoang Thiery
中科院分区：
文献类型：
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作者：
C. Sherlock;Alexandre Hoang Thiery
大多数马尔可夫链蒙特卡罗方法都是在离散时间内进行的，并且相对于目标概率是可逆的。然而，现在可以理解，不可逆马尔可夫链的使用在许多情况下都是有益的。特别是，最近提出的弹跳粒子采样器利用了连续时间和不可逆马尔可夫过程，并且在用于探索某些概率密度时经验地显示了最先进的性能；然而，它的实现通常需要计算对数目标密度的梯度的局部上界。提出了离散弹跳粒子采样器，提出了一种基于导引随机游走、部分方向刷新和延迟拒绝步骤的通用算法。我们证明了弹跳粒子采样器可以理解为我们算法的一种特殊情况的标度极限。与弹跳粒子采样器不同，实现离散弹跳粒子采样器只需要逐点评估目标密度及其梯度。对于目标密度的精确梯度不存在的情况，我们提出了基本算法的扩展。在高斯设置下，我们为径向过程建立了随着维度增加到无穷大的定标极限。我们利用这一结果得到了离散弹跳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谐准则。在更一般的设置中的进一步分析表明，该调优标准适用于更一般的情况。然后比较了不同目标和不同算法变化下的理论效率曲线和经验效率曲线。
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.