Copied from original trac ticket:
Generating and fitting toy experiments where the PDF contains Gaussian constraints is a slightly tricky business. This is discussed in arXiv:1210.7141 and we should try and follow the guidelines therein.
It would seem that the missing piece (wrt what we currently do) is to generate a different value for the mean of the constraint for each toy experiment. Since the PDF construction can change between generation and fitting it would seem to make sense to actually do this in the setup of the fit. But this brings up some concerns about reproducibility. Needs some thought.