An Introduction to Markov Chain Monte Carlo

Abstract

This paper introduces the method of Markov Chain Monte Carlo (MCMC). An outline of the methods is given together with some preliminary tools. The Bayesian approach to statistics is introduced, and the necessary continuous state space Markov chain theory is summarized. Two common algorithms for generating random draws from complex joint distribution are presented; The Gibbs sampler and the Metropolis-Hastings algorithm. We discuss implementational issues and demonstrate the method by a simple empirical example on a generalized linear mixed model. The reader is assumed to have background in probability theory and to be familiar with discrete time Markov chains on a finite state space.