This chapter reviews the recent developments in Markov chain Monte Carlo simulation methods. These methods, which are concerned with the simulation of high dimensional probability distributions, have gained enormous prominence and revolutionized Bayesian statistics. The chapter provides background on the relevant Markov chain theory and provides detailed information on the theory and practice of Markov chain sampling based on the Metropolis-Hastings and Gibbs sampling algorithms. Convergence diagnostics and strategies for implementation are also discussed. A number of examples drawn from Bayesian statistics are used to illustrate the ideas. The chapter also covers in detail the application of MCMC methods to the problems of prediction and model choice.
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ReDIF This chapter was published in: J.J. Heckman & E.E. Leamer (ed.) Handbook of Econometrics, , chapter 57, pages 3569-3649, 2001.
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This chapter was published in the following book, which is listed on IDEAS: J.J. Heckman & E.E. Leamer (ed.), 2001.
"Handbook of Econometrics,"
Handbook of Econometrics,
Elsevier,
edition 1, volume 5, number 5.
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