Seeking Application of Markov Chain Monte Carlo in Different Fields

The Markov Chain Monte Carlo (MCMC) methods build the Markov chain which the stable distribution matches the expected distribution It can approximate sampling and estimate to the complex probability distributions by generating dependent samples iteratively. The MCMC methods are algorithms used to generate samples in the complex probability distributions. This article introduces the basic principles, theory background and the applications of MCMC in various fields such as Bayesian inference, statistical physics, and machine learning. By discussing the particular challenge that MCMC is facing now and the future research directions of MCMC, this paper is focused on providing a comprehensive overview about MCMC methods. And this discussion also emphasizes the historical development of MCMC, its mathematical foundations, and its practical implications in modern computational science. Thus, MCMC methods make the field of computational statistics different and continue to play a key role in the modern data science. As the development of the increasing of computing power and new algorithm, the potential of MCMC will expand further.