Evaluate historical predictions relative to FS

[diazrenata]

Closely related to #17.

See theories and predicted distributions collected https://onlinelibrary.wiley.com/doi/full/10.1111/j.1461-0248.2007.01094.x. How close are the predictions to the empirical in terms of their positions within the feasible set?

This gets complex because you're kind of mixing approaches. Many of these predictions are idealized distributions, not actual vectors of counts. Most draws from some of these distributions don't sum to the state variables.

I have previously tried evaluating the likelihood of all samples from the feasible set, from the predicted distribution, and then seeing if the empirical vector has the highest likelihood. I think this tells us if the predicted distribution is pointing at hollow curves in the feasible set generally, or at specifically the empirical hollow curve. But note that winning in this sense is more like a Venn diagram...the empirical is at the intersection of things-predicted-by-the-distribution and the feasible set.