Markov Chain Monte Carlo and Related Topics

This article provides a brief review of recent developments in Markov chain Monte Carlo methodology. The methods discussed include the standard Metropolis-Hastings algorithm, the Gibbs sampler, and various special cases of interest to practitioners. It also devotes a section on strategies for improving mixing rate of MCMC samplers, e.g., simulated tempering, parallel tempering, parameter expansion, dynamic weighting, and multigrid Monte Carlo with its generalizations. Other related topics are the simulated annealing, the reversible jump method, and the multiple-try Metropolis rule. Theoretical issues such as bounding the mixing rate, diagnosing convergence, and conducting perfect simulations are only brieey mentioned.