Year: 2025
Type: article
Abstract: The Markov Chain Monte Carlo (MCMC) methods have become indispensable tools in modern statistical computation, enabling researchers to approximate complex probability distributions that are otherwise intractable. This paper focus on MCMC in Statistics and Probability area which is used to draw samples from a probability distribution. In order to introduce this algorithm in a relatively light and straightforward way, this paper breaks the content into two parts: Markov Chain and MCMC, and brings in stochastic process, Markov property, Ordinary Monte Carlo, and Monte Carlo Integration in succession. On this foundation, this paper formally introduces two algorithms of MCMC that are Metropolis-Hasting Algorithm and Gibbs Sampling, the most famous and significant algorithms of MCMC. With this approach, this paper concludes both the advantages and disadvantages of these two algorithms, laying the foundation of the further study and the deeper utilizations of MCMC and, hopefully, contributing to providing a certain degree of assistance for scholars.
Source: Theoretical and Natural Science
Author: Qiaomu Liu
Institution: Irvine Valley College
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4409549839