General question on multivariate MCMC diagnostic


I have a quick and general question on the multivariate MCMC diagnostic calculation. Looking at the source code, it appears that the multivariate convergence statistic is not calculated as described in the Brooks, Gelman paper (while the univariate statistics are). Rather than using the scalar distance between the covariance matrix estimates to generate the multivariate stats, it appears that the univariate methodology is being applied to draws of the log posterior (logpo2) in Dynare. Am I reading the code correctly? If so, are the two methods equivalent? Is there any background out there on this calculation, like perhaps a paper I am missing?

Thanks in advance,


Hi, Yes you are correctly reading the code. We have just added a couple of lines in the manual to describe this. The method are not equivalent. We loose the nice property of the Brooks/Gelman approach: our multivariate index is not an upper bound for the univariate diagnostics. But our approach is faster and intuitive.


Okay, thank you for clearing that up! Much appreciated.