On the Random Walk Metropolis Algorithm

Abstract

The random walk Metropolis algorithm belongs to the collection of Markov Chain Mote Carlo (MCMC) methods that are used in statistical inference. It is one of the most common Markov Chain Mote Carlo methods in practical use today. We would like, in this thesis, to introduce the discrete time Markov chains as stochastic processes having the Markov property. We also present some properties of the Markov chains that are needed to the random walk Metropolis algorithm and related to the Markov Chain Mote Carlo methods such as the detailed balance, irreducibility, and aperiodicity properties .And we introduce the random walk as stochastic process,and present some examples of the random walk having the Markov property. We will introduce some of the basic algorithms that belong to the Markov Chain Mote Carlo methods, and we explore the theoretical properties of the random walk Metropolis algorithm for certain kinds of target random variables. Theoretical properties of the random walk Metropolis algorithm for certain special classes of target have been investigated extensively. We will also describe and study some of the related derived results that have important practical implications. We will also demonstrate the impact of the random walk Metropolis algorithm for some practical examples using the R programing language in simulation.