I have revisited my approach to deciding if MCMC has run for long enough recently, and I’m collecting some of the relevant material here:
Last time I thought about it: https://healthyalgorithms.com/2010/04/19/practical-mcmc-advice-when-to-stop/
Original paper for R_hat approach: http://www.stat.columbia.edu/~gelman/research/published/itsim.pdf
Presentation comparing several approaches: http://www.people.fas.harvard.edu/~plam/teaching/methods/convergence/convergence_print.pdf
Published comparison: http://www.jstor.org/stable/2291683
Blog about a cool visual approach: http://andrewgelman.com/2009/12/24/visualizations_1/
Discussion on cross-validated: http://stats.stackexchange.com/questions/507/what-is-the-best-method-for-checking-convergence-in-mcmc
Book with a chapter on this referenced there: http://www.amazon.com/dp/1441915753/?tag=stackoverfl08-20 (available as an eBook from UW Library, how convenient!)
Another related blog: http://xianblog.wordpress.com/2012/11/28/mcmc-convergence-assessment/
Healthy Algorithms 