Distance between configurations in Markov chain Monte Carlo simulations
Distance between configurations in Markov chain Monte Carlo simulations
复制标题
马尔可夫链蒙特卡罗模拟中配置之间的距离
DOI：
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复制
发表时间：
2017
影响因子：
5.4
通讯作者：
N. Umeda
中科院分区：
文献类型：
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作者：
M. Fukuma;N. Matsumoto;N. Umeda
对于给定的马尔可夫链蒙特卡罗算法，我们引入了两个配置之间的距离，该距离量化了从一种配置过渡到另一种配置的难度。我们认为，对于在配置空间中生成局部移动的算法类别，距离采用通用形式。我们明确计算 Langevin 算法的距离，并表明它确实具有作为距离的期望和预期属性。我们进一步表明，通过引入回火方法，多峰分布的距离从大值急剧减小。我们还认为，当原始分布是高度多峰且具有大量简并真空时，在扩展配置空间中自然会出现反德西特几何。
For a given Markov chain Monte Carlo algorithm we introduce a distance between two configurations that quantifies the difficulty of transition from one configuration to the other configuration. We argue that the distance takes a universal form for the class of algorithms which generate local moves in the configuration space. We explicitly calculate the distance for the Langevin algorithm, and show that it certainly has desired and expected properties as distance. We further show that the distance for a multimodal distribution gets dramatically reduced from a large value by the introduction of a tempering method. We also argue that, when the original distribution is highly multimodal with large number of degenerate vacua, an anti-de Sitter-like geometry naturally emerges in the extended configuration space.
DOI：
10.1088/1742-6596/706/2/022004
发表时间：
2015-12
期刊：
Journal of Physics: Conference Series
影响因子：
--
作者：
G. Aarts
通讯作者：
G. Aarts
影响因子：
2.7
作者：
Aarts, Gert;Bongiovanni, Lorenzo;Stamatescu, Ion-Olimpiu
通讯作者：
Stamatescu, Ion-Olimpiu