Fit bias in HistFactory

Dear experts,

Recently, I tried to do a toy MC study with HistFactory. However, pull distribution always shows minus bias.

Here is the simplified the code which reproduces the problem: (9.2 KB)
This code

  1. make histogram template and work space
  2. fluctuate the nuisance parameter by Normal distribution. Generate toy MC and fit
  3. iterate (2) 10000 times and make pull distribution

If I run the code, I obtain

the mean of pull distribution is -0.088 ± 0.01. There is a bias. Is it expected in Histfactory? Or do I make some mistakes?

Thank you.

Dear @june0812,

Let me invite @jonas or @moneta to help you with your question.


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