The Discussion About The Applications Of Markov Chains

This paper primarily discusses the Markov chains and its applications, Markov chains are stochastic processes with good properties, used greatly in practice. For instance, Poisson process and Brownian motion are continuous-time Markov process. Markov chains are widely used in computational mathematics, economics and finance, humanities and so on, so it is of great use for us to learn about the processes. This paper consists of five chapters, and what I do is in chapter3, that is the discussion of the applications of Markov chains in teaching evaluation. In chapter3, this paper shows the model that we use Markov chains to construct in teaching evaluation, and the shortages that exist in traditional model in detail. For the shortages, the paper shows the new methods to avoid the shortages, and improves the model for a better use. In chapter4, the paper considers Markov chain Monte Carlo methods, and elaborates Metropolis-Hastings algorithm and Gibbs sampler in detail. The charts in the paper show the simulation results effectively. In the end of the chapter, the paper considers the convergence of the sequence of the samples, the discussion is of great use for us to use the sampler methods. In the end of the paper, the paper shows what I have done and what I will do in the future.