A Guide to Exact Simulation
A Guide to Exact Simulation
复制标题
精确模拟指南
DOI：
10.1111/j.1751-5823.2001.tb00478.x
复制
发表时间：
2001
影响因子：
2
通讯作者：
X. K. Dimakos
中科院分区：
文献类型：
--
作者：
X. K. Dimakos
马尔可夫链蒙特卡洛（MCMC）方法用于从复杂的多元分布中采样具有归一化常数，这些分布在实践中可能无法计算，并且直接采样不可行。一个基本问题是确定链的收敛性。 Propp＆Wilson（1996）设计了一种Markov链算法，称为过去的耦合（CFTP），该算法解决了此问题，因为它从目标分布中产生了精确的样品，并自动确定需要运行多长时间。目前，CFTP和其他方法的精确采样是一个蓬勃发展的研究主题。本文回顾了其中一些想法，重点是CFTP算法。引入了耦合和单调CFTP的概念，并在呈现算法的运行时间结果。提出了填充的中断方法（1998年）和默多克与格林的方法（1998年）用于连续分布的精确采样。在贝叶斯图像恢复的情况下，报告了新型的模拟实验，以从Ising模型中进行精确采样，并将结果与标准MCMC进行了比较。结果表明，CFTP至少与标准MCMC相同，通过Raftery＆Lewis方法（1992，1996）监测收敛性。
Markov Chain Monte Carlo (MCMC) methods are used to sample from complicated multivariate distributions with normalizing constants that may not be computable in practice and from which direct sampling is not feasible. A fundamental problem is to determine convergence of the chains. Propp & Wilson (1996) devised a Markov chain algorithm called Coupling From The Past (CFTP) that solves this problem, as it produces exact samples from the target distribution and determines automatically how long it needs to run. Exact sampling by CFTP and other methods is currently a thriving research topic. This paper gives a review of some of these ideas, with emphasis on the CFTP algorithm. The concepts of coupling and monotone CFTP are introduced, and results on the running time of the algorithm presented. The interruptible method of Fill (1998) and the method of Murdoch & Green (1998) for exact sampling for continuous distributions are presented. Novel simulation experiments are reported for exact sampling from the Ising model in the setting of Bayesian image restoration, and the results are compared to standard MCMC. The results show that CFTP works at least as well as standard MCMC, with convergence monitored by the method of Raftery & Lewis (1992, 1996).