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Metropolis-hastings adaptive algorithm and its application

Ruoxi Xu

Open publisher page 5 citations

Abstract

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.

About this research paper

What this paper is about

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.

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Available abstract

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.

Key concepts: Metropolis–Hastings algorithm, Markov chain Monte Carlo, Bayesian probability, Algorithm, Computer science, Markov chain, Rejection sampling, Random walk

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