Mathematical Foundations of the Markov Chain Monte Carlo Method
Mathematical Foundations of the Markov Chain Monte Carlo Method
复制标题
马尔可夫链蒙特卡罗方法的数学基础
DOI：
10.1007/978-3-662-12788-9_4
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发表时间：
1998
影响因子：
0.5
通讯作者：
M. Jerrum
中科院分区：
文献类型：
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作者：
M. Jerrum
马尔可夫链蒙特卡罗（MCMC）方法利用的想法，一组组合对象的信息可以通过执行适当定义的随机游走这些对象上获得。在统计物理学领域，MCMC算法已经使用多年，用于估计各种物理量，通常是统计模型“配置”上的随机变量的期望。MCMC算法的运行时间取决于随机游走收敛到平衡点的速度;只有当达到接近平衡的条件时，算法才能发现“典型”对象是什么样的。在过去的十年左右，它已经成为可能，以获得一个先验界的速度收敛到平衡的随机游动基本MCMC算法的实际利益。在无法推导出先验界限的情况下，仍然有可能进行严格接地的实验。许多主要的思想和技术在这里列出，最近的发展正在讨论更长的时间。
The Markov chain Monte Carlo (MCMC) method exploits the idea that information about a set of combinatorial objects may be obtained by performing an appropriately defined random walk on those objects. In the area of statistical physics, MCMC algorithms have been in use for many years for the purpose of estimating various quantities of physical interest, often expectations of random variables on “configurations” of a statistical model. The running time of MCMC algorithms depends on the rate at which the random walk converges to equilibrium; only when a condition of near-equilibrium has been achieved can the algorithm discover what “typical” objects are like. In the past decade or so, it has become possible to derive a priori bounds on the rate of convergence to equilibrium of random walks underlying MCMC algorithms of practical interest. In cases where a priori bounds cannot be derived, it may still be possible to conduct rigorously grounded experiments. Many of the main ideas and techniques are set out here, with the recent developments being discussed at greater length.