Do you know of any good beginner tutorials for Stan or probabilistic programming in general? All the examples that I found seemed quite complex and I was a bit overwhelmed by all the math. Which might also be a sign that I should brush up my math skills. What kind of math/stats should I revise to be able to better understand probabilistic programming?
Probabilistic Programming & Bayesian Methods for Hackers [1] by Cameron Davidson-Pilon is exactly what you want, starting from a computational-first perspective, then introducing the maths later, although it uses PyMC rather than Stan. It's freely available as a set of Jupyter notebooks, as well as a printed edition.
Doing Bayesian Data Analysis, Second Edition: A Tutorial with R, JAGS, and Stan. It is very approachable and also has lots of practice problems. It's not a math-heavy book at all.
Edit: I wouldn't recommend Probabilistic Programming and Bayesian Methods for Hackers. When I tried using it, I felt that too much was glossed over. The book that I recommend excels at conveying a strong intuition for how these various techniques work.
That's the foundation. The way you set up your model is by nodes and edges that specify the flow of influence (directed or undirected). Then it seems that there are general methods for inference and learning on any kind of graph one might pose.
For simple graphs (and simple is something one might want when modelling) the methods should be fairly effective.
Unfortunately, the biggest book on the subject that I know (Koller & Friedman) isn't accessible. Koller's course is also not that accessible.
