Multicanonical MCMC for sampling rare events: an illustrative review
Multicanonical MCMC for sampling rare events: an illustrative review
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DOI：
10.1007/s10463-014-0460-2
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发表时间：
2014-06-01
影响因子：
1
通讯作者：
Kitajima, Akimasa
中科院分区：
文献类型：
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作者：
Iba, Yukito;Saito, Nen;Kitajima, Akimasa
讨论了多典型马尔可夫链蒙特卡罗(MCMC)作为稀有事件抽样的一种方法。首先回顾了重要性抽样的一般框架，然后介绍了多正则MCMC在随机矩阵、随机图和混沌动力系统中的应用。副本交换MCMC(也称为并行调和或城域耦合MCMC)也被解释为多规范MCMC的替代方案。最后，将多标准MCMC应用于数据代理，并给出了一个成功的时间序列代理实现。在附录中，讨论了指数族的平均值和归一化常数的计算、相共存、模拟回火、并行化和多元扩张。
Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is introduced, followed by applications in random matrices, random graphs, and chaotic dynamical systems. Replica exchange MCMC (also known as parallel tempering or Metropolis-coupled MCMC) is also explained as an alternative to multicanonical MCMC. In the last section, multicanonical MCMC is applied to data surrogation; a successful implementation in surrogating time series is shown. In the appendix, calculation of averages and normalizing constant in an exponential family, phase coexistence, simulated tempering, parallelization, and multivariate extensions are discussed.