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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.

For details of Monte Carlo methods, theorems and proofs and a full list of references, the reader is directed to Neal (1993), Gilks, Richardson and Spiegelhalter (1996), and Tanner (1996).