Awesome, thanks for the hint. I’ve tried the pseudo prior approach and it works really well for avoiding the sampling problem.
I still wonder, if there is a way to make the step-wise inference work, or if it is valid in the first place. I feel like I’m making a simplification there that doesn’t work.
In any case, i’ve written up a little notebook that includes both the pseudo-prior and the VI solution for my models, in case that’s interesting for anyone.