WILEY SERIES IN PROBABILITY AND STATISTICS The second edition attempts to capture significant developments in EM methodology in the ten years since the publication of the first edition. The basic EM algorithm has two main drawbacks-slow convergence and lack of an in-built procedure to compute the covariance matrix of parameter estimates. Moreover, some complex problems lead to intractable E-steps, for which Monte Carlo methods have been shown to provide efficient solutions. There are many parallels and connections between the EM algorithm and Markov chain Monte Carlo algorithms, especially EM with data augmentation and Gibbs sampling. Furthermore, the key idea of the EM algorithm where a surrogate function of the log likelihood is maximized in a iterative procedure occurs in quite a few other optimization procedures as well, leading to a more general way of looking at EM as an optimization procedure.