Fit with finite statistics

Joel found this paper, which I think describes exactly what we need. I'm going through it at the moment trying to figure out how to apply it.

There is a root implementation, TFractionFitter, but in one dimension. That could be used by just putting everything in one dimension e.g. instead of a 10x10 bin histogram have a 100 bin histogram. I also found this page which says there are problems with the implementation (although it's unclear for which root version). One of the comments says that there is an implementation in RooFit that works properly though, so I'll have a look at that.