Following up on this, I tried just building a very simple heteroscedastic GP like you describe.
I think these treedepth things could just be a result of how much data is being fit. If I fit a single condition2 dataset for one person, all the treedepths are exceeded and I get posterior draws of mean and standard deviation that look like:
If I artificially limit how much data I’m passing it, I don’t get those warnings. For instance, I just used 5 trajectories of the same data I got no warnings and the posterior samples of mean and standard deviation look like:
This has just been bothering me cause by the pictures it seems like the model should work. Could just be as simple as you have a ton of data and so all the parameters are very tightly constrained.