Practical examples are a great place to start when learning Bayesian computational techniques.
The Stan case studies here are complex but well-documented: https://mc-stan.org/users/documentation/case-studies.html
Michael Betancourt’s case studies are also excellent: https://betanalpha.github.io/writing/
The rstanarm vignettes are simpler, but give a good lay of the land: http://mc-stan.org/rstanarm/articles/index.html
Eventually, you’ll find yourself needing to tackle the behemoth that is the Stan manual. It used to be one 400-page pdf, but they split it into three (which you can also read in html online):
The User’s Guide: https://mc-stan.org/docs/2_19/stan-users-guide/index.html. Fantastic examples of just about every type of model you could want to fit in Stan, and programming tips for making your models better.
The Language Reference Manual: https://mc-stan.org/docs/2_19/reference-manual/index.html. See some weird syntax? Look it up here.
The Functions Reference: https://mc-stan.org/docs/2_19/functions-reference/index.html. Want to know what a particular distribution’s function is call, and what the parameters are? This will tell you.
Bayesian statistics, particularly the computational side, is a fast-moving field. Because of that, blogs by leading Bayesian statisticians are a great way to stay up to date.
Andrew Gelman and others involved in the Stan project run this excellent blog about Bayesian statistics: https://statmodeling.stat.columbia.edu/
As an example, have a look at this blog post by Dan Simpson, about the Gelman-Rubin diagnostic \(\hat{R}\):
What he’s saying won’t make sense yet, but it will! And, eventually, it’ll be implemented in Stan for the rest of us to use.
Richard McElreath, author of Statistical Rethinking, also has a blog with a few really good posts: http://elevanth.org/blog/
We’ll use some of them as references for later labs. He also records lectures based on his book, in case hearing things in a different way is helpful to you: https://www.youtube.com/channel/UCNJK6_DZvcMqNSzQdEkzvzA