From deviance, DIC, AIC, etc., to leave-one-out cross-validation

Maren Vranckx writes:

I am writing in connection with a post on your blog on 22 June 2011 about “Deviance, DIC, AIC, cross-validation, etc”. In this post, you mentioned that you and a student worked about DIC convergence. Can you specify how you did the research? Did you discover a reason for slow convergence of DIC? Was the slow convergence for specific disease data? In which book is the example of zillion iterations to have convergence DIC stated? Did you perform research about this more recently?

My reply:

Some of our more recent thinking on this topic is here and here.

It’s good to know that we’re making progress in our understanding.