Resumen
Many commonly used models in statistics can be formulated as (Bayesian) hierarchical Gaussian Markov random field (GMRF) models. These are characterised by assuming a (often large) GMRF as the second stage in the hierarchical structure and a few hyperparameters at the third stage. Markov chain Monte Carlo (MCMC) is the common approach for Bayesian inference in such models. The variance of the Monte Carlo estimates is Op(M-1/2) where M is the number of samples in the chain so, in order to obtain precise estimates of marginal densities, say, we need M to be very large.