I am curious too. I have used Stan extensively. I found it extremely polished and pleasant to use.

It generated very efficient samplers for particularly weird (and enormous!) hierarchical models I had. Documentation is also great.

It is also worth reading Andrew Gelman's post about Prophet: https://statmodeling.stat.columbia.edu/2017/03/01/facebooks-...

I think he just means that it can be an incredible pain to install.

Not directly from machine learning perspective, rather touching stability of use in production setup. We at VictoriaMetrics allow Prophet to be one of the models to use for time series anomaly detection in vmanomaly product. When it comes to cloud environment, Prophet, which uses `cmdstanpy` under the hood, allows little to no control over the backend, thus, resulting in unexpected crashes for read-only filesystems like Red Hat OpenShift, after the backend attempts to create assets in /tmp directory during model fit stage, so such dependencies may limit usage of a product in real-world scenarios.