I implemented a a Gibbs Sampler for a hierarchical model with priors and hyperpriors that has around 16 variables.

When it comes to autocorrelation plots, I have seen in some papers that they do not plot all the variables, but it's not clear to me how they chose the subset of variables to plot.

Is there some good practice about which variables to report (for a paper in a computational statistics journal)?

For instance, my model performs a clustering and has a Dirichlet Process on top. Is this enough to plot the autocorrelation of the concentration parameter of the Dirichlet Process or should I also plot the other variables?

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    $\begingroup$ There is no reason to select some parameters/variables among your 16 variables. You should plot all of them to check for a possible lack of divergence. $\endgroup$ – Xi'an Jan 19 '16 at 9:26
  • $\begingroup$ Thanks Xi'an, you could make it an answer, this is exactly what I was looking for :) $\endgroup$ – alberto Jan 19 '16 at 9:57
  • $\begingroup$ PS: @Xi'an since you are here: what about multidimensional variables (multidimensional means, covariance matrices...)? $\endgroup$ – alberto Jan 19 '16 at 9:58
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    $\begingroup$ Easy: Multivariate variables can be broken into univariate variables. $\endgroup$ – Xi'an Jan 19 '16 at 13:58
  • $\begingroup$ Let me bring your attention on this related question: stats.stackexchange.com/questions/185923/… $\endgroup$ – alberto Jan 19 '16 at 14:30

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