Using Bayesian model diagrams to present both model description and results (posteriors)?

Question

The model diagrams in "Doing Bayesian Data Analysis", John Kruschke creates diagrams like this:

To represent The following BUGS/JAGS code:

He discusses this representation in his related blog post, Graphical model diagrams in Doing Bayesian Data Analysis versus traditional convention

I just wrote one out for my rather complicated model and had a real moment of clarity.

The diagrams are generic representations of probability density functions- they don't really reflect the flat priors stated in the model (although technically, the x-axes are not labeled).

I haven't actually read the book, but I think it would be even more useful to use this diagram to present both the model structure and the results, i.e., replace these generic distributions with the posterior probability density of each parameter (e.g. $\textrm{N}(\textrm{figure of }M_0,\textrm{ figure of }T_0)$ (rather than a single distribution to represent both parameters as is the case below.

I have three questions:

1. Are there any potential technical (statistical) issues with this approach? I only ask because I haven't seen results presented alongside the model description in this way.
2. Are there any other suggestions for how to make this do a great job of communicating results? One idea that I had was to present an indexed beta (e.g. a random effect for 1...n categorical treatments, in the model above it would be beta1[i]) as overlapping densities (one for each treatment effect)?
3. How could I make this presentation be more intuitive to readers not familiar with hierarchical modeling? (I think this is the most intuitive presentation that I have found so far, but there may be room for improvement)

Answer 1

Thanks for your question. I'm glad that the style of diagram helps people "have a real moment of clarity." I concur from personal experience: For me to really understand a model, I have to make a diagram of it like these.

The diagrams are intended to communicate the structure of the prior and likelihood. For that purpose, iconic distributions are better than particular choices of hyperprior constants.

For example, the iconic gamma, with its sharply descending curve on the left, communicates instantly that the distribution is limited on the left but has infinite extent to the right. If instead it showed a gamma(0.01,0.01) or whatever, it would be too easy to visually confuse with an exponential distribution.

Similarly, the iconic beta distribution instantly communicates that the distribution is limited on both ends. If instead it showed an "uninformed" Haldane prior, approximated by beta(0.0001,0.0001), it would be a confusing squarish U-shaped distribution with spikes at the two ends, that might even be visually confused with a Bernoulli distribution.

Thus, the iconic distributions do a good job for their intended purpose.

It would not be appropriate to display the posterior this way because the marginals on the posterior are not necessarily shaped like any particular basic distribution. For example, a gamma prior on a parameter need not yield a gamma-shaped marginal posterior. Moreover, although the priors on the parameters are independent in the JAGS model, the posterior distribution usually has correlations among parameters.