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Toy generation with constraints should follow guidelines in arXiv:1210.7141
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First reported in the 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 (or means in the case of multi-dimensional constraints) from the constraint PDF for each toy experiment being fitted.
We need to do this only when fitting toy, so need a mechanism to distinguish that case from a fit to data.

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