I am new to the pymc and thinking with probabilities.
I have checked out a few of the basic hierarchical pooling tutorials: radon and rugby.
I am interested in understanding the extended hierarchical pooling found in where they “move up” in the level.
https://docs.pymc.io/pymc-examples/examples/case_studies/multilevel_modeling.html
In this example, after they have modeled the “floor” by “county” relationship, they move on to take into account a “country” level in the example.
I am however interested in a more “sibling approach”. For instance, I surmise (and pretend I have data for the following).
- Rainfall by county. I believe that rainfall can “wash away” radon in the ground as it trickles through.
While, we could say that this is just an input variable into the Normal distribution, I wish for the relationship between amount of Rainfall and radon to be variable by county, related, but can fluctuate.
In the physical world, I would explain that by saying, the effects of rainwater in loose-soil vs solid granite is different, but would still expect that 5 inches of rain per week to have more of an effect than 1 inches of rain per week.
How can I modify the existing radon example to incorporate such "county level " if I only want to include this type of rainfall data?
Am I even asking the question correctly?
– btw I cannot add soil type as an input, because I don’t have it…which is why I want to let it find it’s own loosely related values.