I’ve been performing some simulation studies comparing a Bayesian to a more traditional frequentist estimation approach in a particular problem. To do this I’ve been using the excellent JAGS package, calling it from R. One of the issues I’ve faced is the question of how long to run the MCMC sampler in the Bayesian approach. Use too few iterations, and the chains will not have converged to their stationary distribution, such that the samples will not be from the posterior distribution of the model parameters. In regular data analysis situations, one can make use of the extensive diagnostic toolkit which has been developed over the years. The most popular of these is I believe to examine trace plots from multiple chains, started with dispersed initial values, and also Gelman and Rubin’s Rhat measure.