# Beeston Barlow light math in HistFactory manual

Dear experts,

I am trying to work through the Beeston Barlow light math in Section 2.2.1 of https://cds.cern.ch/record/1456844/files/CERN-OPEN-2012-016.pdf

If the total statistical uncertainty in bin b is defined as delta_b, and the MC yield in that bin is nu_b, the relative uncertainty should be (delta_b/nu_b)? (The text has the reciprocal of this, as a typo I suspect).

Then the equivalent yield which has the same relative stat. unc. as above should be m_b = (nu_b/delta_b)^2 (Again, the text has the reciprocal).

Finally, the text defines another parameter called tau_b = (nu_b/delta_b)^2. To me this is the same as what m_b is supposed to be, and I don’t see the point of this new parameter. If so, the Poisson constraint term (the second term in eqn 9) becomes

Pois(m_b | gamma_b * m_b)

meaning that the “expected” value of gamma_b is 1. Am I understanding this correctly?

I am writing not to criticize the helpful paper, but rather to make sure I understand the math.

Thanks a lot,
Arvind.

Pinging to keep this thread alive.

I tried to read through and understand the Beeston Barlow code (ROOT: roofit/histfactory/src/RooBarlowBeestonLL.cxx Source File), and I see that the code does have two separate parameters for m_b and tau_b, and gets them in different ways. But it is not immediately clear to me what the difference between these two parameters is.

Best,
Arvind.

Hi @avenkate ,
sorry for the lack of reply, we need @moneta or @jonas to make progress, let’s ping them.

Cheers,
Enrico

Hi,

I think you are right, in the text there is a wrong definition of `m_b`. Actually the definition of `tau_b` is correct, `m_b` is a global observable, corresponding to the amount of total MC bin sample size.
The `gamma_b` is just a factor, centred around 1 to express the uncertainty of this MC bin size. It will come in the likelihood with a corresponding constraint term. The value of `tau_b` is instead the expected contribution of the MC and it is considered fixed.
I hope this clarify the difference between `m_b` , `gamma_b` and `tau_b`

Cheers

Lorenzo

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