Does separating data and Monte Carlo statistical uncertainties cause double counting?

[ChrisVer]

Hi
I was wondering the following/feeling uneasy about it:
Does it make sense to separate the statistical uncertainties of data and Monte Carlo?
For example assume infinite statistics in your MC (uncertainty-->0) while your data is finite : so they come with some "uncertainty" (if that makes sense for an observation).

Then, exchange the two cases, aka consider the observation a fixed number (which sounds reasonable to me) and vary the MC within its uncertainty.

Doesn't the combination of those two steps result in double counting? (I have a feeling that that is happening).

 

[mfb]

They are two different uncertainty sources, and both influence separately (and differently!) how well you can estimate the physical parameter you are looking for.

 

[mathman]

Monte Carlo uncertainty is a reflection of the computational model precision. Physical uncertainty reflects physics not mathematics.