Hug and hop: a discrete-time, nonreversible Markov chain Monte Carlo algorithm
Hug and hop: a discrete-time, nonreversible Markov chain Monte Carlo algorithm
复制标题
拥抱和跳跃：离散时间、不可逆马尔可夫链蒙特卡罗算法
DOI：
10.1093/biomet/asac039
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发表时间：
2023
期刊：
影响因子：
2.7
通讯作者：
Ludkin M
中科院分区：
文献类型：
--
作者：
Ludkin M
本文介绍了拥抱和跳跃马尔可夫链蒙特卡罗算法估计的期望值与一个棘手的分布。该算法在两个内核之间交替，称为hug和hop。拥抱是一个不可逆的内核，它重复应用最近提出的弹跳粒子采样器的弹跳机制，以产生一个远离当前位置但几乎位于目标密度相同轮廓上的建议点，从而导致高接受概率。Hug由hop补充，hop故意提出轮廓之间的跳跃，并且具有随着维度的增加而非常缓慢地降低的效率。hug和使用蛙跳积分器的Hamilton Monte Carlo之间有许多相似之处，包括积分方案的顺序，但hug也能够利用局部Hessian信息而无需隐式数值积分步骤，并且其性能最终不会受到对数后验的无界梯度的影响。我们在各种玩具目标和真实的统计模型上对拥抱和跳跃进行了经验测试，发现它可以而且经常优于汉密尔顿蒙特卡罗。
This article introduces the hug and hop Markov chain Monte Carlo algorithm for estimating expectations with respect to an intractable distribution. The algorithm alternates between two kernels, referred to as hug and hop. Hug is a nonreversible kernel that repeatedly applies the bounce mechanism from the recently proposed bouncy particle sampler to produce a proposal point that is far from the current position yet on almost the same contour of the target density, leading to a high acceptance probability. Hug is complemented by hop, which deliberately proposes jumps between contours and has an efficiency that degrades very slowly with increasing dimension. There are many parallels between hug and Hamiltonian Monte Carlo using a leapfrog integrator, including the order of the integration scheme, but hug is also able to make use of local Hessian information without requiring implicit numerical integration steps, and its performance is not terminally affected by unbounded gradients of the log-posterior. We test hug and hop empirically on a variety of toy targets and real statistical models, and find that it can, and often does, outperform Hamiltonian Monte Carlo.