系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2008年
1期
100~108
,共null页
MCMC Metropolis—Hastings算法 马尔可夫链 R软件 贝叶斯分析
MCMC Metropolis—Hastings算法 馬爾可伕鏈 R軟件 貝葉斯分析
MCMC Metropolis—Hastings산법 마이가부련 R연건 패협사분석
MCMC; Metropolis-Hastings algorithm; markov chain; R software; bayesian analysis
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．
首先闡述Metropolis-Hastings算法實現的具體步驟，然後證明由此產生的Markov鏈滿足細緻平衡條件，從而以目標分佈為不變分佈．接下來給齣幾箇計算實例，以說明提議函數及其方差的選取對採樣結果的影響，併由此推齣一種改進的自適應算法用以尋找閤適的提議函數及其方差．最後，通過貝葉斯Logistic模型的例子說明M-H方法在貝葉斯分析中的應用，同時也檢驗M-H自適應算法的效果．
수선천술Metropolis-Hastings산법실현적구체보취，연후증명유차산생적Markov련만족세치평형조건，종이이목표분포위불변분포．접하래급출궤개계산실례，이설명제의함수급기방차적선취대채양결과적영향，병유차추출일충개진적자괄응산법용이심조합괄적제의함수급기방차．최후，통과패협사Logistic모형적례자설명M-H방법재패협사분석중적응용，동시야검험M-H자괄응산법적효과．
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.
