can anyone provide examples of practical use of Stan in the business arena?
For instance, can you predict website user navigation, or product sales with Stan?
Furthermore, how does Stan compare with other probabilistic programming languages such as Figaro?
I just read and can recommend
There is also a post by @andrewgelman in response to the above: How smartly.io productized Bayesian revenue estimation with Stan
There are gazillions of uses of Stan in business. We don’t tend to have pre-canned models for web analytics, though, if that’s what you’re looking for.
You can check out Facebook’s open-source system Prophet, which is based on Stan. It’s specifically aimed at time-series forecasting with seasonal and weekly and holiday effects like you’d use for predicting product sales.
I’m not sure what Figaro’s used for. Their tutorial doesn’t get very far into real modeling and I don’t know what other resources are out there.
If you’re keen on Scala, you can also check out ScalaStan. CiboTech built it and is using it for crop prediction (computational agronomy).
This is probably my favorite example of a ‘pure’ business problem being solved in STAN: http://phasedchirp.github.io/2016/09/12/bayesian-inference-for-nps.html