Hi, @Nicklaus_Millican:
As your outlines hints, there are really two things going on here: teaching Bayesian statistics and teaching Stan (and even teaching programming). There are two “official” resources that might help here:
- Stan Reference Manual: full details on how the language works
- Stan User’s Guide: a guide to programming in Stan
The Reference Manual is written for programmers and is rather dry and also not quite as precise as a formal specification. The User’s Guide is intended for people who already know Stan and already know Bayesian stats and want to know how to translate pieces of a model into Stan. It should have probably been called a “Programmer’s Guide”. As you point out, we don’t really have an intro and didn’t want to try to add too much tutorial material to either of the above docs. We really should put a short intro to the language into the User’s Guide. If you wanted to write that and submit it to Stan on GitHub (stan-dev/docs, written in Quarto), we could add it to the docs. We’re pretty picky in reviewing, but welcome contributions and will help with revisions.
CRC/Chapman & Hall keep asking us to write The Stan Book along the same line as their The BUGS Book. So if you really do fill out this overview, you have a clear route to publication! The closest I’ve come is this introduction:
I plan to go back and fill in more material. And maybe have someone translate to R :-).
@andrewgelman, @avehtari, and a host of others are working on a Bayesian workflow book that is essentially unfolding and trying to make sense of the paper:
- Gelman et al. Bayesian workflow (arXiv)
There are a lot of online resources including videos and replicable case studies on the Stan site (both just listed under case studies and in the StanCon proceedings, which also have videos linked in most cases).
There are also several books that are more tutorials oriented. We have a list here:
- Stan web site: Books related to Stan
Richard McElreath’s book is a great place to start if you’re new to Bayesian statistics and MCMC, and I believe there are matching videos online.
- McElreath. Statistical Rethinking
It’s woefully out of date, though I occasionally update it. There’s also an intro book by Bruno Nicenboim, Daniel Schad, and Shravan Vasishth. I reviewed a large chunk for the publisher, CRC, and it’s both really solid and tutorial oriented (a rare combination):
- Nicenboim et al. An Introduction to Bayesian Data Analysis for Cognitive Science