Metropolis-hastings adaptive algorithm and its application
Ruoxi Xu · Systems Engineering - Theory & Practice · 2008
Markov chain Monte Carlo(MCMC) methods is an important class of computer based simulation techniques.This paper investigates one MCMC method known as the Metropolis-Hastings algorithm.In this paper,we first introduce readers the proceedings of the Metropolis-Hastings algorithm.Then we prove the resulting chain satisfies detailed balance,and hence has the target distribution as the invariant distribution.Next,we provide some illustrative examples that show the influence of the proposal function and its variance on the resulting chain,and develop an adaptive method to find optimal proposal for the random walk sampler.Finally,we discuss the relationship between M-H algorithm and Bayesian analysis.The Bayesian Logistic model is used to illustrative the application of M-H algorithm in Bayesian analysis and to test the proposed adaptive method.