I have just registered because a message from Bob. First of all I must confess that I have very little knowledge (or if you prefer I have very big ignorance) about Stan. I’m researching on non-linear dynamics in economics and I am looking for a way to calibrate a non-linear model http://www.sciencedirect.com/science/article/pii/S0378475416000045 on real data. Therefore, now, I am on this forum to understand whether this can be achievable. I found this paper “Automatic Differentiation Variational Inference” http://www.stat.columbia.edu/~gelman/research/unpublished/advi_journal where it is mentioned advi integrated into Stan. But, again, my understanding/knowledge is very little at the moment. Suggestions/proposals are more than welcome.
Usually the thing to do if you have a model that you want to fit in Stan is code up the simplest model you can manage, generate some data from it, and then try to fit that data in Stan. You can do all of that with Stan models (generating the data in Stan may seem a bit weird, but it’ll help you make sure you’re fitting data to the same model you’re generating it from).
I think the ADVI stuff is considered experimental at this point. You’ll be better off just running Stan in its default mode to start and let NUTS do the sampling.
I clicked on that model and looked at the abstract/some of the pictures. It’s kind of scary looking honestly. I’m no expert, but you might have a better time if you look for a model of this process from a more statistical standpoint to start with. It’s my understanding that chaotic ODEs do really weird funky things and have mean sensitivities that produce random-like behavior (that’s why they are chaotic). I think most ODE modeling in Stan is done by assuming you have a really well behaved ODE and then have noisy measurements around that (which is pretty different).
Just scrolled around the paper some more, I think I spoke too soon. There’s no ODEs here.
It looks more like they’re modeling differences in a time series rather than the whole time series together itself. This will be way more feasible! Have a look at the Time Series model section in the Stan manual for some similar stuff. Sorry for the confusion!