Study Of MCMC Method

This paper considers the Markov Chain Monte Carlo methods mainly the Metho-plis algorithm and the Gibbs algorithm introduces the process of these algorithm. analyze the convergence of the Markov Chain ,discuss the problem of assessing the error of MCMC methods . In the end we discuss the application of MCMC methods in hierarchical Bayesian mode. The first section mainly introduces the static state Monte Carlo methods mainly introduces frequency methods and expectation methods also discuss the problems of how to improve the precision in these methods .The second section mainly introduces two examples of MCMC methods i.e. Metroplis algorithm and Gibbs algorithm ,include the detailed process of these algorithm and the relation of these algorithm .we also discuss how to improve these algorithm in application .The third section mainly introduces three aspect of MCMC method i.e. convergence,error,and strategy. We discuss the realizations of three hypothetical Markov Chain in the problem of convergence .We also discuss how to reduce the error of Monte Carlo estimates .In the end of this section we discuss how to choose a appropriate strategy in a simulation runs .The fourth section mainly introduces the application of MCMC methods in Bayesican mode.