Hi to anyone, I was looking at some blog posts on hierarchical models for variational inference for numpyro, and was confused on what the posterior distribution should be for these kind of models. An example of that is here, Finally! Bayesian Hierarchical Modelling at Scale - Florian Wilhelm's blog, where the posterior q(disp_params) is a function of q(disp_params_mu) and q(disp_params_loc) which are its parents in the graphical model. However, in some other cases in pyro, it seems that the posterior does not need to be a function of its parents as in the forum post here. Simple Hierarchical Guide - #2 by fehiepsi. I was wondering if this is a design choice or is one of them preferable? Also, which kind are the autoguides be using?

I got another question for the autoguide AutoHierarchicalNormalMessenger. I didnt really understand the following sentence.

The mean-field posterior at any site is a transformed normal distribution, the mean of which depends on the value of that site given its dependencies in the model:

loc_total = loc + transform.inv(prior.mean) * weight

Is this another design choice?