Add intuitive glossary of common terms

[abner-hb]

I think that it would be good to add an accessible glossary of some common parameters and summary outputs. Many users struggle to understand and even find explanations of terms they see often, like Rhat, bulk and tail effective sample sizes (ESS), sampling iteration, tree depth, and even chains. Most of these terms have technical explanations scattered throughout the libraries documentation or the Stan guide. But having a single reference with more intuitive explanations would help everyone, especially applied users from fields other than Statistics.

[bob-carpenter]

Thanks for opening the issue @abner-hb. Where do you think this should go? We tend to put this kind of thing in the Reference Manual because it applies across all of our interfaces. If we do that, we should pointers to that discussion in our doc for the interfaces.

The User's Guide is mainly about writing models and doesn't talk at all about inference. I've often thought it'd be good to add an intro to how Stan works up front that's a little less dry and officious than our Reference Manual.

[abner-hb]

I find it a bit strange that the User's Guide section on Posterior Inference & Model Checking does not even mention things like like Rhat and ESS.

I think this glossary would fit well as an appendix of the User's Guide. Mostly because I think that new users like to begin by seeing how to write a simple model (which the Guide shows for several models) and how to read the output (which the glossary would facilitate).

If not there, then I think the glossary could fit somewhere in the Reference Manual. In part because a glossary seems a literal reference resource (like a regular dictionary); and in part because the Algorithms section talks the most about many of the terms I mentioned.

I also like your idea of having a more lively intro. But I think this would require fully working examples and I'm not sure how this could be done in an interface-agnostic way.