MCMC教程1：An introduction to Markov chain Monte carlo methods and their actural application

[编者的话]

MCMC方法是一种重要的模拟计算方法，马尔可夫链蒙特卡尔理论(Markov chain Monte Carlo：MCMC)的研究对建立可实际应用的统计模型开辟了广阔的前景。90年代以来，很多应用问题都存在着分析对象比较复杂与正确识别模型结构的困难。现在根据MCMC理论，通过使用专用统计软件进行MCMC模拟，可解决许多复杂性问题。此外，得益于MCMC理论的运用，使得贝叶斯(Bayes)统计得到了再度复兴，以往被认为不可能实施计算的统计方法变得是很轻而易举了。以前，MCMC主要在物理学中应用，而现在大量生物信息学问题的解决都和MCMC相关了，在这一期，编者向大家推荐三篇教程，希望对大家掌握这一方法有所帮助，这里是第一篇的摘要。

This paper introduces the readers of the Proceedings to an important class of computer based simulation techniques known as Markov chain Monte Carlo (MCMC) methods. General properties characterizing these methods will be discussed, but the main emphasis will be placed on one MCMC method known as the Gibbs sampler. The Gibbs sampler permits one to simulate realizations from complicated stochastic models in high dimensions by making use of the model’s associated full conditional distributions, which will generally have a much simpler and more manageable form. In its most extreme version, the Gibbs sampler reduces the analysis of a complicated multivariate stochastic model to the consideration of that model’s associated univariate full conditional distributions. In this paper, the Gibbs sampler will be illustrated with four examples. The first three of these examples serve as rather elementary yet instructive applications of the Gibbs sampler. The fourth example describes a reasonably sophisticated application of the Gibbs sampler in the important arena of credibility for classification ratemaking via hierarchical models, and involves the Bayesian prediction of frequency counts in workers compensation insurance.

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