Metropolis-Hastings自适应算法及其应用  

Metropolis-hastings adaptive algorithm and its application

作　　者：陈平[1] 徐若曦[2] 

机构地区：[1]东南大学数学系,南京210096 [2]俄亥俄州立大学统计系,美国43210-1247

出　　处：《系统工程理论与实践》2008年第1期100-108,共9页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(10671032)

摘　　要：首先阐述Metropolis-Hastings算法实现的具体步骤,然后证明由此产生的Markov链满足细致平衡条件,从而以目标分布为不变分布.接下来给出几个计算实例,以说明提议函数及其方差的选取对采样结果的影响,并由此推出一种改进的自适应算法用以寻找合适的提议函数及其方差.最后,通过贝叶斯Logistic模型的例子说明M-H方法在贝叶斯分析中的应用,同时也检验M-H自适应算法的效果.Markov chain Monte Carlo （MCMC） methods is an important class of computer based simulation techniques. This paper investigates one MCMC method known as the Metropolis-Hastings algorithm. In this paper, we first introduce readers the proceedings of the Metropolis-Hastings algorithm. Then we prove the resulting chain satisfies detailed balance, and hence has the target distribution as the invariant distribution. Next, we provide some illustrative examples that show the influence of the proposal function and its variance on the resulting chain, and develop an adaptive method to find optimal proposal for the random walk sampler. Finally, we discuss the relationship between M- H algorithm and Bayesian analysis. The Bayesian Logistic model is used to illustrative the application of M-H algorithm in Bayesian analysis and to test the proposed adaptive method.

关 键 词：MCMC Metropolis—Hastings算法 马尔可夫链 R软件 贝叶斯分析 

分 类 号：F830[经济管理—金融学] TP183[自动化与计算机技术—控制理论与控制工程]