I understand RStan is maybe the main interface to Stan, but I’m not a big fan of R, and barely have any libraries installed to do anything beyond plotting heatmaps.
I had seen some of those links, although I have yet to read the paper on the math library (not sure I’ll have time soon, but it’s on my list).
I don’t think it’s all that different from what other people asked above. Unless you just really like C++ and want to be able to do the exact same thing RStan or PyStan do, the advantage of C++ is you would be able to start using Stan from somewhere downstream from the model specification, and possibly bypass anything it is not prepared to do.
For instance, if it can’t handle numerical solutions because I could provide a function that returns an array with the prediction, and use provide numerical gradients, or whatever other wacky handling of the model you may want to implement, at your own risk of messing it up.
Packages like PyMC3 apparently moved to be more Stan-like than its previous version, which allowed a more generic implementation of your f(\theta) and specification of the likelihood [say p(y|\theta) = Poisson(f(\theta))] - and that would be all you needed to feed to the sampler. But that just won’t do it anymore.
I would otherwise just write down the likelihood and gradients, code the model and sampler from scratch in any one language (whether it is Python, C++, Julia, or whatever) and run it.
I feel like that is overkill, and extra effort to implement a lesser version of what Stan does very well, so ideally I’d be able to join the community and take advantage of all the work you have already done. I’m not a developer or a statistician, so maybe some of this doesn’t really make sense to you. Thanks for the reading list, again.