Keywords: markov chain, monte carlo, convergence, diagnostic
When do you stop running a Markov chain Monte Carlo (MCMC) simulation? Many researchers turn to the Gelman-Rubin (GR) convergence diagnostic, which calculates a statistic based on the variance within chains and the variance between chains. Since its introduction, researchers have improved methods of variance estimation for Monte Carlo averages. Incorporating these improved estimators into the GR statistic results in more stable MCMC termination time and MCMC averages, easy implementation for a single chain, and economical computational efforts in the multivariate setting. This talk will introduce you to updated GR statistics for the univariate and multivariate settings, teach you how to easily select a principled cutoff criterion (rather than the frequently-used criterion of R = .1) using a newly-discovered relationship between the GR statistic and effective sample size, and illustrate the advantages of these methods by presenting results from simulations and real world data analysis. Sample R code will be included.