Introduction to Monte Carlo Methods

Abstract

This chapter describes a sequence of Monte Carlo methods: importance sampling, rejection sampling, the Metropolis method, and Gibbs sampling. For each method, we discuss whether the method is expected to be useful for high--dimensional problems such as arise in inference with graphical models. After the methods have been described, the terminology of Markov chain Monte Carlo methods is presented. The chapter concludes with a discussion of advanced methods, including methods for reducing random walk behaviour.