本文主要介绍了马尔科夫链蒙特卡洛（MCMC）方法的原理以及关于马氏链采样的收敛诊断，并针对于一类特殊的目标分布给出了高效的蒙特卡洛模拟策略。传统的MCMC方法是指Metropolis-Hastings算法，该算法具有一定的局限性，当后验概率分布维数高，形式复杂时，算法收敛慢。以此为背景，本文以相关系数为0.99的二元正态分布作为目标分布，利用改进的MCMC方法，如Gibbs算法，MALA算法和MTM算法等进行抽样，比较抽样效果，得出结论为MALA算法对这类分布的抽样效果最好，该算法的接受率大致为0.48。

This Paper mainly introduces Markov Chain Monte Carlo methods and the convergence diagnosis of Markov sampling. Some efficient Monte Carlo simulation strategies are proposed for a given special target distribution. The traditional MCMC method refers to Metropolis-Hastings algorithm which has some limitations. When posterior probability distribution is in a high dimensional space and complicated, the convergence speed is slow. In this context, the target distribution is bivariate normal distribution whose correlation coefficient is 0.99. We make sampling by improved MCMC methods, such as Gibbs algorithm, MALA algorithm and MTM algorithm. The result is that MALA algorithm is best sampling method for this kind of distribution by comparing with other algorithms above and its acceptance rate is approximately 0.48.