This paper reviews and develops the applications of Markov chain Monte Carlo methods in pedigree analysis, with particular stress on the Metropolis algorithm. In likelihood based genetic analyses, standard deterministic algorithms often fail because of the computational complexity of the observed pedigree data under a proposed genetic model. The new Monte Carlo methods permit approximate maximum likelihood estimation in the presence of such complexity. Monte Carlo implementation of the EM algorithm is the key to successful maximum likelihood analysis. Gibbs sampling and the Metropolis algorithm are alternative ways of defining Markov chains for performing the E step of the EM algorithm. Two applications illustrate the power and simplicity of the Metropolis algorithm. One of these applications involves a discrete model for variance component analysis of quantitative traits; the other application involves a Monte Carlo version of location scores for multipoint linkage analysis.
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