Hi iavicenna,
Thank you for the detailed response! I’m glad to hear that my approach at least seems reasonable from a modeling perspective. Also, thank you for the model corrections, shifting to a lognormal group mean seems like a better option. I have a couple of questions regarding your implementation and suggestions.
by double counting of mean, do you also mean using mean in both mean and sd? In that case some of the suggestions I said above could be helpful.
Yes, if the likelihood sd is specified as a function of the mean and its inherent uncertainty multiplied by the CoV uncertainty, then I would imagine the posterior variance would be in some sense double counting mean variance. I’m still new to bayesian modeling, so perhaps this isn’t the case or it isn’t really an issue.
Another alternative could be using lognormal instead of normal where the amount of sd will naturally depend on mu.
I’m not sure I understand this correction, could you expand on this a little?
[A]re you generating the data like this because that is what you suspect the model is like or do you have good reason to think it works that way?
Yes, looking at historical data, I have reason be believe that each group shares a common coefficient of variation with potential for some mild deviations from the common CoV. Under a limited sampling scenario it is easy to under or overestimate the variance, so my hope is to borrow predictive power from similar groups for specifying variation of a group with few samples. I specified the group level CoV variance as a prior (rather than a learned variable) so as to impart domain knowledge of deviance from the common CoV.
One thing I have notice is you do get about ~200 divergences in 40000 samples even with target_accept=0.95. So perhaps re parametrizing could help there too.
Reparameterizing in what sense? Forgive my ignorance.
And thanks for the reference as well, I’ll be sure to give that read!