# Geweke Diagnostics in Bayesian regression model

I'm a newbie in Bayesian modelling and trying to understand something more on such field by running a Poisson regression and analyzing count data.

Browsing on the internet, I found a set of diagnostics for assessing the model convergence; among all of these ones, I read about the Geweke's diagnostics.

I know it rejects the hypothesis of convergence for large z-score, but I wonder of how much the z-score has to be large to reject the hypothesis. There exists a rule of thumb?

Moreover, in the case one has a really large z-score, let's say 3, what you could do? I read about one has to have a longer chain, but I really did not get what does it mean.

Could you provide some help, possibly by providing a reference about?

The Geweke diagnostic is pretty simple. It compares the mean of the samples drawn from the end of a chain of MCMC output to the mean of the samples at the beginning of the chain using a $z$-test like statistic. The variance of the two means is computed using spectral densities (b/c the MCMC output is not independent).
As for a cut-off you can compare to the standard normal critical values $z_{\alpha/2}$ where $\alpha=0.05$ or something similar.