Custom uncertainty models that can account for down revisions #369
Description
Problem
Sometimes reports are down-revised, which appear as negative values in the reporting triangle. In terms of fixing the point estimates, these are preprocessed away (which is I think necessary for this model) but it would be nice not to assign probability zero to generating them probabilistically, which the neg. bin. default uncertainty model does by construction.
Feature request
Its possible to extend the uncertainty model already e.g. the branch getting PRed here CDCgov/nowcastNHSN#12 . However, it would be nice to have some of these uncertainty models available when step 1.2 of #229 happens. My proposed other models would be:
- Normal, rounded to int possibly.
- Skellam, that is the difference of two Poissons with seperate means.
For situations with fairly low numbers of reports the Skellam distribution would seem to intuitively represent a situation when you have poisson distribution report arriving at some ref-date/lag combo with another poisson distributed number of reports that get revised down due to whatever reason.
Possible solution
Both the distributions above are one-parameter once you fix the mean as the point prediction and the free parameter can be estimated using MLE (as per fit_nb) and then sampled from (as per sample_nb).