A.F.M. Smith, G.O. Roberts, "Bayesian computation via the Gibbs sampler and related Markov-Chain Monte-Carlo methods," Journal of the Royal Statistical Society Series B, 55:3-23, 1993.
Gareth Roberts (Statistical Laboratory, University of Cambridge, England): "The Markov-Chain Monte-Carlo (MCMC) methodology has been around for more than 40 years. However, until recently, its applications have been largely confined to statistical physics and image analysis.
"A very natural area of application of these techniques, especially the Gibbs sampler and the Hastings-Metropolis algorithm, is in numerical calculations for larger-dimensional posterior distributions in Bayesian statistical analyses. Our paper brings together the MCMC methodology with its natural application in Bayesian statistics. We describe the basic technique and discuss some of the important implementational and convergence issues associated with the algorithms--which necessarily produce correlated output, even after 'convergence'--from both a theoretical and a practical point of view. Key areas of application are highlighted, including problems with constrained parameters, ...
