quite often when I set up a hierarchical model in in pymc3 I encounter the following problem: My lower-level parameters (e.g., subject-level parameters) are drawn from higher-level distributions (e.g. group-level parameters). Now quite often I have parameters on the lower level that are not supposed to take negative values. In a non-hierarchical version, I can use direct priors that establish this bound. But how do I proceed in the hierarchical version, where I typically use Normal distributions between the group and subject level? Here are a few more detailed questions/ideas:
a) Can I use bounded Normals instead? I often use a non-central parametrization (https://twiecki.io/blog/2017/02/08/bayesian-hierchical-non-centered/). Can I simply add a min() operation to the deterministic calculation of the normally distributed values?
b) Should I rather use a log-Normal to link the subject and group level? How would I have to transform the parameters?
c) Or should I (log-?) transform the data?
I know the question is not pymc3 specific per se. But I believe there are some expert here who hopefully could help and I’d be very happy about some pymc3 specific solutions.
Many thanks in advance!