@bob-carpenter the post correction capability of DADVI is one aspect that I really like and would want to apply. The paper also mentions the possibility to check whether the current sample size for the SAA approximation is sufficient, so that a successful check can be used to stop the (outer) iteration (over the sample size). But I have no practical experience and will have to see how it performs and how useful the computed approximations are.
Thanks a lot for highlighting the need for running additional checks. I have already seen that the mean field approximation has significant bias for the across group variation of e.g. slopes in a hierarchical linear model (when running on synthetic data from.a generative model). But at least the population slopes were somewhat correctly captured. Its defintively not ideal and I am already wary of how it will perform when I try to move from a linear to a nonlinear setting.