Application of Markov chain Monte carlo method in Bayesian statistics

Abstract

In statistical inference methods, Bayesian method is a method of great influence. This paper introduces the basic idea of the Bayesian method. However, the widespread popularity of MCMC samplers is largely due to their impact on solving statistical computation problems related to Bayesian inference. Markov chain Monte Carlo method is essentially a Monte Carlo synthesis procedure. The random sample of it is related to a Markov chain. It is a widely used stochastic simulation method. This paper mainly introduces Gibbs sampling, and its application in Bayesian statistics. We use a simple example to illustrate how to tackle a typical Bayesian problem via the MCMC method.