Thanks for this nice paper emphasizing the importance of multilevel hierarchical modeling. You mention here that these methods can be generalized to arbitrary (e.g. non-gaussian) distributions. Have you investigated or thought about what distributions might result at the higher level?

I noticed a few years ago that across fields, "almost-Cauchy" distributions with power-law tails best describe the (dis)agreement between different measurements (see Not Normal: the uncertainties of scientific measurements. Power laws are ubiquitous in complex systems (such as scientific measurements), but their origins are still not well understood, so new ideas are always welcome.