Understanding Hierarchical models

[bob-carpenter]

If you have four different hyperprior parameters, \mu_1, \ldots, \mu_4 and \sigma_1, \ldots, \sigma_4, then they will almost always get different values (the probability of them having the same values is technically zero outside of initialization). This is because the hyperpriors are treated the same way as other parameters in ADVI or MCMC.