Markov Chain Monte Carlo Method And Implemented With R

Ordinary Monte Carlo provides a convenience for computing some complex integration with stochastic simulation method. But when it isn’t easy for direct sampling, the concept of Markov chain is introduced into the sampling. And the non-periodic and irreducible Markov chain can converge to stable invariant distribution. When Markov chain has been running long enough, we think that the Markov chain sequence is generated from a random sample of the target distribution. Thus, Markov Chain Monte Carlo method has emerged, and it is also the so-called MCMC.This article focuses on the theoretical basis and construction principles of MCMC, which makes this method to be better recognized and accepted. The first part of this paper introduces principles of simple simulation Monte Carlo and analyzes how to narrow error of Monte Carlo integration. Combined with mathematical knowledge and reasoning of Markov chains, the second part describes the theoretical basis of MCMC methods, construction method and its convergence analysis. In this part, I firstly present the structure and principles of MCMC method, and focuses on the Metropolis-Hastings algorithm and Gibbs sampling. When MCMC algorithm is analyzed, the algorithm code is written through statistical software R-language as result to a better analytical result which includes graphical diagnostics and parameter estimation results, and then discusses the convergence and error of MCMC. The third part discusses the application of MCMC into Bayesian statistics. Derived posterior distribution parameters of samples f(/β|y) corresponds to the Metropolis-Hastings algorithm of Logistic regression model, and gave a case with the R language to be computing, and get a better diagnostic parameter estimation. Finally, this paper tries parallel algorithm of MCMC so that MCMC algorithm could be applied well to large samples or large data.