I found the posterior distribution of sigma via MCMC obey Normal distribution, which seems not influenced by the prior distribution.
But in SVI, set the right posterior in guide() is important and difficult . So I choose Normal distribution (inspired by MCMC results ). But I found it may sample negative value for sigma
I find my problem is quite similar with Setting constraints and guides on constrained distributions.
Does this mean that svi is not applicable in hierarchical Bayesian ?