Remember and note that
The posterior mean and posterior SD are the most used statistics to summarise MCMC output and to provide parameter estimates. The small command-line tool pbayz (supplied with bayz) makes different (small, large, selected) parameter-summaries by computing mean and SD of the saved samples. Details are explained on the page Summaries with pbayz.
Note: the posterior mean is not always the best summary statistic, for instance, it may not reveal that a variance has a large probability density near zero when it has large uncertainty (has a wide long-tailed distribution). Adding additional statistics such as mode, median and HPD (see below) can be useful.
Sample output from bayz can be imported in R, which provides a flexible way to compute parameter statistics that go beyond the simpel mean and SD from pbayz, to plot densities, and computer posterior mean and SD for functions of model parameters. See the page Summaries with R
By importing the MCMC output in R, convergence diagnostics and estimates of Monte Carlo error can be obtained using the R coda package. See the page on Using R coda.
One way to compare models with bayz is to compute the Deviance Information Criterion, see the page Computing DIC.