Hi Lewis,
Yes I think you should go the hierarchical road if you wanna share information between globes.
I think I’d start with something like:
with pm.Model() as planet_model:
a = pm.Exponential("a", 1)
b = pm.Exponential("b", 1)
p_globes = pm.Beta("p_globes", a , b, shape=n_globes)
w = pm.Binomial("w", p=p_globes, n=total_observations, observed=water_observations)
This is just a raw idea of course. There is a good notebook about hierarchical models on PyMC’s website (note that this tutorial has been updated but is not yet deployed on the website).
Hope this helps 