A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms
A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms
复制标题
平行回火和无限交换算法某些定性性质的大偏差分析
DOI：
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发表时间：
2016
影响因子：
1.8
通讯作者：
P. Nyquist
中科院分区：
文献类型：
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作者：
J. D. Doll;P. Dupuis;P. Nyquist
并行回火或副本交换是模拟复杂系统的常用方法。这个想法是在不同的温度下运行并行模拟，并以给定的交换率在并行模拟之间交换配置。从大偏差的角度来看，最优的是让互换率趋于无穷大，并且可以构造相应的模拟方案，称为无限互换。在本文中，我们提出了一种新的使用大偏差的经验措施，更详细的分析无限交换限制设置连续时间跳马尔可夫过程。使用大偏差率函数和相关的随机控制问题，我们认为诊断的基础上的温度分配，这可以很容易地计算在模拟。我们证明了这个诊断收敛到它的先验已知极限是无限交换收敛的必要条件。率函数也被用来调查潜在的景观中的不对称性的影响，以及在状态空间中最有可能发生差采样。
Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. We show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. The rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.