MCMC算法及其应用

MCMC Algorithm and Its Application

摘要: 本文主要介绍了马尔可夫链蒙特卡罗方法(MCMC)，主要是Metropolis方法、Hasting方法和Gibbs方法。介绍了这些算法的基本步骤，同时利用马尔可夫链的收敛性，讨论了算法的误差，并对算法进行改进。最后，给出了极限性质一些简单的应用。本文主要分为六部分：第一部分介绍了马尔可夫链的性质。第二部分主要介绍了Metropolis-Hasting (M-H)算法及推广，介绍了两种特殊的MCMC算法，即Metropolis算法和Hasting算法以及算法的实现过程。第三部分介绍了建议概率分布的改进，降低了误差，提高了收敛性。第四部介绍了Gibbs算法以及贝叶斯模型。第五部分给出了实例与应用，同时在众多方法中找到一个合适的实施方法。最后一部分，也就是第六部分进行了总结。

Abstract: This paper mainly introduces the Markov Chain Monte Carlo Method (MCMC), which is mainly the Metropolis method, Hasting method and Gibbs method. The basic steps of these algorithms are in-troduced. At the same time, the convergence of Markov chain is used, the error of the algorithm is discussed, and the algorithm is improved. Finally, some simple applications of the limit properties are given. This paper is divided into six parts: The first part introduces the nature of the Markov chain. The second part introduces the Metropolis-Hasting (M-H) algorithm and promotion, and in-troduces two special MCMC algorithms, namely Metropolis algorithm and Hasting algorithm and algorithm implementation process. The third part introduces the improvement of the proposed probability distribution, which reduces the error and improves the convergence. The fourth part introduces the Gibbs algorithm and the Bayesian model. The fifth part gives examples and appli-cations, and finds a suitable implementation method among many methods. The last part, the sixth part, is summarized.